Question: Is the star mentioned in Acts 7:43 ("you lifted up the star of your god Rephan") the star of David?
Response: One thing I can say with dogmatism about Acts 7:43 is that the star is not the star of David. For one thing, the star of David as a Jewish national symbol is a fairly recent invention (not much older than the USA), and there is, as far as I know, nothing in the archaeological artifacts or texts from the days of ancient Israel to suggest that the six-pointed star symbol was even in existence prior to the modern era (let alone being an important ancient symbol).
Stephen is quoting here from Amos 5:25-26, but he is quoting from the Greek Septuagint version rather than the Hebrew. This question of what is meant here becomes a little clearer if we translate the Hebrew of verse 26 in full:
For you lifted up the shrine of your king (i.e., pagan god), and the pedestal of your idols, [even] the star of your gods which you made for yourselves.
As this verse indicates, in addition to the Lord's tabernacle and furnishings, Israel had also secretly carried about the paraphernalia of their former idols (a fact which accounts for the many failings and the insincerity of faith in that first generation "whose bones were scattered in the wilderness": 1Cor.10:5). This is of course not unprecedented as we are reminded of Rachel's theft of her father's idols (Gen.31:19), and the need for Jacob to cleanse his family of such things at God's command (Gen.35:4 NIV: So they gave Jacob all the foreign gods they had and the rings in their ears, and Jacob buried them under the oak at Shechem").
The phrase "[even] the star of your gods" is a difficult one, but it clearly applies to the shrine and the pedestal both. That is, "[even] the star of your gods" sums up the accouterment of idolatry that the rebellious Israelites kept in their kit to worship the pagan gods whom they had not entirely rejected in favor of the Lord (as the golden calf incident illustrates very well).
Why the use of the word "star" to describe this idolatrous paraphernalia? I would suggest several reasons:
1) all idolatry is at its base satanic angel worship (a fact which helps to account for the close connection between idolatry with astrology, witchcraft and magic), and the angels (fallen angels included) are often referred to as stars (cf. Judg.5:20; Job 38:7; Is.14:13-14; 40:26 w. Lk.2:13):
"At that time," says the Lord, "they will bring out the bones of the kings of Judah, and the bones of its princes, and the bones of the priests, and the bones of the prophets, and the bones of the inhabitants of Jerusalem from their graves. They will spread them abroad to the sun and to the moon and to the whole host of the heavens (i.e., here both fallen angels and the stars that represent them are in view), which they have loved and served and after whom they have followed and consulted and whom they have worshiped".
2) There is also a clear reproach in Amos 5:8-9 to Israel. All who received this communication from Amos would have been well aware that the true Star of God was the coming Messiah (Num.24:17), the One they were not looking to during the Exodus and still not looking to during Amos' day, but turning instead to pagan "stars" instead of to the true Star of God (2Pet.1:19; Rev.22:16; cf. Num.24:17; Is.9:1-2; 42:6; 49:6; Matt.2:2; 2:9; 4:16; Lk.2:30-32; Jn.1:4-5; 8:12; 9:5).
3) Stars also refer to glory (cf. 1Cor.15:40-44), so that with these words Amos tells the Israelites that they had exchanged their true glory, the Lord, for the false glory of the idol (exactly what Paul says at Rom.1:22);
4) Finally, in verse eight of chapter five, Amos has reminded his hearers that it is God who made the constellations, let alone individual stars, so that this reference a bit later in the chapter to a lone star clearly shows the Israelites that they had chosen to worship a very small part of the creation instead of the Creator who made everything, including all the innumerable stars (also Paul's point in Rom.1:25).
The reason for the Septuagint's odd translation is twofold:
1) In the Masoretic text, the Hebrew words "tabernacle" and "pedestal" are spelled normally as to their consonants, but as to the vowel points (which are all later than the consonantal text), instead of using the correct pronunciation, the later scribes in both cases supplied the vowels appropriate to the word shiqutz or "abomination". This is a very familiar device in the Old Testament, employed both to avoid pronouncing the name of the pagan deity and also to degrade all such mentions of idolatry (cf. beelzebub in place of Ba'al Zabhul: "lord of flies" instead of Ba'al the Lofty, as Thomas Kelly Cheyne has pointed out; see also A. Fruchtenbaum on this). This alteration of the vowel points, a scribal euphemism to avoid blasphemy, was apparently confusing to the translators of the Septuagint.
2) The word "pedestal" begins with the letter chaph ("ch"), a consonant which is very close in the old Semitic script to the letter rhesh ("r"). Confused by the spelling in the text of his Hebrew exemplar, the LXX translator was probably reminded of the name of the pagan god "Rephan" (i.e., prob. "Saturn") in some variation so that this is what he wrote (but again we have him copying the degrading vowel points of shiqutz: "Riyphun").
Stephen's use of the Septuagint quotation which has "Moloch" instead of "king" (again, both words employ the same consonants in Hebrew) and "Rephan" instead of "pedestal" serves to make the connection with idolatry much more clear than a straight translation of the Hebrew would have done. We may consider this a sanctified interpretation of the original verse that brings the point home through the ministry of the Spirit with even more force than it otherwise would have had.
Please also see the discussion at the following link:
The star of David is not the star of Rephan (in "Christians Beware: Internet Frauds")
Hope this is of some help.