Also, since Acts is thrown about a lot at this point, along with claims that the author claimed this or that, let's clear that up a bit.
The bulk of Acts is basically written by the same gLuke that wrote the gospel. In fact, it's the sequel to the gospel. It starts directly where the gospel ends.
(And since at that point they had a trilogy of gospels, and his name was Lucas, we can only be thankful that he didn't decide to do a prequel trilogy

)
Not only he says so, but it's the same style, down to word usage and whatnot. So yeah, that's gLuke writing it.
EXCEPT it's not all of it. There are whole chunks, and big ones at that, that don't match his style at all, and make claims that conflict with the rest of it in some way or another.
One example are the "we" sections, where essentially the author becomes some protagonist that travelled with Paul. Not only the style doesn't match, or in what person it's written doesn't match, but basically it contradicts that 'great historian' claim that gLuke makes at the beginning of the gospel. There he claims to have researched this kinda stuff, while here he's travelling and meeting with first hand witnesses. Why didn't he make THAT claim about his sources, if that were the case.
Another are the 'trial records'. When people like Peter or Stephen speak in court in Acts, it's a completely different style than gLuke's. Those are definitely not written by the same person that wrote most of Acts.
So at this point there are two main 'theories' among scholars about WTH is with those sections. They're as following:
1. Luke, being such a great historian that he has to say so himself, copied those from earlier texts. Like, he found some speech by someone in court, and just copied it there. Or found some earlier source from someone who actually travelled with Paul, and just copied those pages verbatim.
And it wouldn't even be hard to imagine that Luke is a plagiarist, since most of his Gospel is copied verbatim from Mark and Q. (Whatever Q was. Some make a convincing case that it could have been simply Matthew.)
2. Later forgery.