Albert Barnes Commentary Acts 7:37

"This is that Moses, who said unto the children of Israel, A prophet shall God raise up unto you from among your brethren, like unto me." — Acts 7:37 (ASV)

This refers to what was said in Deuteronomy 18:15, 18 (see this explained in Acts 3:22). Stephen introduced this to remind them of the promise of a Messiah, to show his faith in it, and particularly to remind them of their obligation to hear and obey Him.

The prophecy described a prophet like unto me (that is, "as myself"). It also declared, him shall ye hear (Matthew 17:5).