Thus far, there has been no explicit mention of a brother. The only information we have on any immediate family of the Doctor is:
- Susan, his granddaughter, who appears regularly in the first ten serials or so (season one and start of season two).
- A great-grandson by Susan, who appears only in some Eighth Doctor audio episodes
- His mother, who appears (not acknowledged on-screen, but has since been confirmed) in the Tenth Doctor's final season finale.
- Jenny, his cloned offspring, whom he has acknowledged as his daughter.[1]
Presumably he has at least one natural son/daughter, Susan's parent, but we are never told which.
Of course, if you buy the New Adventures novels, then Time Lords aren't born, they're "loomed" in batches of 40-50, all of which are called "cousins", but its usually best to just pretend that stuff never happened.
[1]: As @Mr. Lister correctly points out, Jenny is not strictly a "clone" of the Doctor; she was produced by some unspecified replication process based on his DNA, but obviously including some genetic variations. She appeared physiologically to be Gallifreyan, so it's not clear where the alterations to her DNA came from. Calling her a "daughter" is probably the closest term we can come in English.