The Doctor has done so more than once.
- In "The Adventuress of Henrietta Street" (BBC Eighth Doctor Adventures novel), the Eighth Doctor married Scarlette.
- In "The Day of the Doctor", the Tenth Doctor married Queen Elizabeth I of England.
- In "A Christmas Carol", the Eleventh Doctor said that he had married Marilyn Monroe.
- In "The Wedding of River Song", the Eleventh Doctor married River Song. Although the improvised ceremony was apparently unofficial & the Doctor was inside the Teselecta during it, the Doctor, River & River's parents (the Ponds) all regarded the marriage as valid. While River had some Time Lord characteristics, she was an "enhanced human" & her parents were human.
The Doctor has implied there were other marriages, too, but we know little about them. This list of human spouses may therefore be incomplete.