We know that since the Third Year (PoA), Hagrid is fully cleared of all charges and allowed to do magic, and therefore presumably to own a wand.
Is there some canon/JKR info on why he didn't bother getting a wand?
The 2 most obvious explanations - both popular with fans and seemingly neither clearly supported by canon or Word of JKR - are:
The wand in his umbrella is already fixed (by Dumbledore using the Elder Wand) long time ago, and the problems he has doing magic pre-PoA are simply his poor skills due to having been expelled in 3rd year and not being a great student.
Again, him not being a great student, he wouldn't have the aptitude or at least the desire to re-learn to do magic with a wand now that he managed just fine without one all his life.