Needless to say, they've never actually shown a Time Lord penis on TV, but the males almost certainly have them.
In "Doctor Who" the TV movie, Grace Holloway saw the Seventh Doctor naked. Granted, she doesn't seem to be a very good doctor, but I think she would have noticed a difference that obvious.
In "The Doctor Dances", the Ninth Doctor told Rose and Jack that his people "dance", meaning have sex, with humans. There are other ways to dance (as Jack surely knows), but look how defensive he was getting—if he weren't equipped for the bog-standard way, he would have addressed that.
In "The Eleventh Hour", Amy Pond watched the Eleventh Doctor undress. She's the kind of girl who would have noticed, and commented, if his equipment were nonstandard. And she presumably wouldn't have come on to him a few episodes later, either. Rory, who is a nurse, also got a brief glance, and didn't freak out and yell "What's that thing?"
Finally, Time Lords are shaped like humans externally in every way that we can see. They have 10 fingers, not 12 or 8. The females have breasts, the males have adam's apples, and so on. Unless otherwise specified, I think it's safe to say that the males also have penises.