Hagrid’s father was a human who had a child, Rubeus Hagrid, with a giantess named Fridwulfa. After Fridwulfa abandoned her family when Rubeus was very young, Mr. Hagrid raised his half-giant son as a single father. He died while Rubeus was a second-year at Hogwarts (GF23).
Other canon notes and references
One of Rubeus Hagrid's worst memories was of his father's death (PA11).
Species / Race Wizard (presumably)
Family Groups Hagrid family
Nowhere in canon does it state that Hagrid's father was a wizard, although it seems likely since Muggles don't even know that giants exist.
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