The first half of the Book of Acts is concerned primarily with the church in Jerusalem, viewed as the center from which evangelizing forces went out into the world. The background of the narrative is obviously Judean. It is antecedently probable that the earliest documents of this Jewish-Christian community would have been written in Aramaic, the vernacular. We also have excellent reason for believing that Luke, the compiler of the two histories, was one who made special search for Semitic documents, as the primitive and authentic sources, in order to render them into Greek. I think I may claim, without undue presumption . . . that the compiler of the Third Gospel was an accomplished translator of both Hebrew and Aramaic. We shall therefore surmise, at the outset, that the very noticeable Semitic coloring of the first part of the book, remarked by all commentators, is simply due to translation.
It is not necessary to argue that the Greek of Acts is not homogenous; it may be well, however, to review here the main facts touching the question of translation. For the first fifteen chapters, the language is distinctly translation-Greek; in the remaining chapters, on the contrary, the idiom is not Semitic, and there is no evidence that we are dealing with a version. The whole book, however, shows unmistakable uniformity of vocabulary and phraseology so that it is obvious (to him who recognizes the Semitic source) that the author of 16-28 was the translator of 1-15. Many have remarked that the most strongly "Hebraizing" chapters are those at the beginning of the book. The reason for this appearance is the fact that the opening chapters are so largely made up of speeches composed in high style, along with quotations from the Old Testament.
from pages 4-5, Composition and Date of Acts