LXX Gen 15:13-14 (cf. Ex 2:22, 3:12)
ἐλάλησεν δὲ οὕτως ὁ θεὸς ὅτι ἔσται τὸ σπέρμα αὐτοῦ πάροικον ἐν γῇ ἀλλοτρίᾳ καὶ δουλώσουσιν αὐτὸ καὶ κακώσουσιν ἔτη τετρακόσια· 7 καὶ τὸ ἔθνος ᾧ ἐὰν δουλεύσουσιν κρινῶ ἐγώ, ὁ θεὸς εἶπεν, καὶ μετὰ ταῦτα ἐξελεύσονται καὶ λατρεύσουσίν μοι ἐν τῷ τόπῳ τούτῳ.
Gen 15:13-14 καὶ ἐρρέθη πρὸς Αβραμ Γινώσκων γνώσῃ ὅτι πάροικον ἔσται τὸ σπέρμα σου ἐν γῇ οὐκ ἰδίᾳ, καὶ δουλώσουσιν αὐτοὺς καὶ κακώσουσιν αὐτοὺς καὶ ταπεινώσουσιν αὐτοὺς τετρακόσια ἔτη. 14 τὸ δὲ ἔθνος, ᾧ ἐὰν δουλεύσωσιν, κρινῶ ἐγώ· μετὰ δὲ ταῦτα ἐξελεύσονται ὧδε μετὰ ἀποσκευῆς πολλῆς.
Exod 2:22 ἐν γαστρὶ δὲ λαβοῦσα ἡ γυνὴ ἔτεκεν υἱόν καὶ ἐπωνόμασεν Μωυσῆς τὸ ὄνομα αὐτοῦ Γηρσαμ λέγων ὅτι πάροικός εἰμι ἐν γῇ ἀλλοτρίᾳ
Exod 3:12 εἶπεν δὲ ὁ θεὸς Μωυσεῖ λέγων ὅτι ἔσομαι μετὰ σοῦ καὶ τοῦτό σοι τὸ σημεῖον ὅτι ἐγώ σε ἐξαποστέλλω ἐν τῷ ἐξαγαγεῖν σε τὸν λαόν μου ἐξ Αἰγύπτου καὶ λατρεύσετε τῷ θεῷ ἐν τῷ ὄρει τούτῳ
Acts quotes primarily from God's promise to Abraham in the LXX of Gen 15:13-14 (words in bold print). The words in green are paralleled in Exod 2:22 (the birth of Moses' son Gershom), and the final clause (in orange) draws on God's promise to Moses at the burning bush.
I suspect πάροικον ἐν γῇ ἀλλοτρίᾳ is simply an unintentional substition of a familiar phrase from Exod 2:22 for Gen 15:13's πάροικον ... ἐν γῇ οὐκ ἰδίᾳ.
However, I think the allusion to Exod 3:12 at the end is an intentional telescoping of two distinct promises, and I suspect Luke expected his audience would pick up on it. (Notice the repetition of 'place' in 7:33, the reference back to 7:6 in 7:34, and the extensive attention to the burning bush at the turning point of the speech in Acts 7:30-34.) Instead of promising Abraham 'great possessions' as in Gen 15:14, God tells Abraham that the purpose of the exodus is worship--one of the main concerns of the Stephen speech.
- This leads to ambiguity about the place of worship: Is it the land (from Abraham's perspective), Mt. Sinai (from the perspective of the burning bush), or, as Greg Stirling has suggested, both: “The implication is that there is more than one holy place…the Temple is holy, but so is Mount Sinai.”*
- It also suggests--against the majority of Luke-Acts scholars--that Luke combined the Abrahamic and Mosaic covenants, since the purpose of both was to worship God "in holiness and righteousness...all our days" (Luke 1:73-75; Acts 7:7).
In both instances, worship becomes idolatry when God's people refuse to listen.
*Sterling, Gregory E. "'Opening the Scriptures': The Legitimation of the Jewish Diaspora and the Early Christian Mission," Pages 199-225 (here 214) in Jesus and the Heritage of Israel: Luke's Narrative Claim upon Israel's Legacy. Edited by David P. Moessner. Harrisburg, PA: Trinity Press International, 1999.