Can same-sex couples marry in a church?

Yes. In jurisdictions where same-sex marriage is legal, the ceremony can be performed by a civil authority (e.g., judge, justice of the peace) or by registered clergy.

The only thing that could prevent a same-sex couple from marrying in a church is if the hierarchy of the church has promulgated doctrine condemning same-sex marriage. This has happened in some Christian denominations, but not in others. The individual clergy members of such a denomination would likely not be willing to permit a same-sex marriage ceremony to take place in their church, either because they themselves oppose it or because doing so would subject them to discipline from the church hierarchy.

It is important to note that many denominations not only permit same-sex marriage, but will also ordain clergy who themselves are parties to a same-sex marriage.
This depends on where you live. In places where same-.sex marriage is legal it's not always allowed in a church with the whole wedding ceremony. In some places you are allowed to get a blessing in church.
Most Christian Churches do not perform same sex marriages. It is usually a non religious ceremony, performed by a secular person allowed to marry people.. It is a very rare Christian Church that will perform a same sex marriage.