In his commentary on the book of Acts, Darrell Bock offers a helpful explanation of how repentance and faith in Jesus relate with one another:
Repentance and faith are two sides of the same coin.
Repentance to God represents a change of direction in how one relates to God. It entails faith in Jesus, so that the turning results in one placing trust in what God did through Jesus as one embraces his person and work.
There is a good reminder here that repentance is ultimately about God and how we relate with God. Therefore, repentance isn't simply a turning from sin, but also a turning to Jesus, in faith. A 'gospel' that demands the former and disregards the latter is no gospel at all.