Yes, Hagrid was in the Order of the Phoenix. Dumbledore, as the leader of the Order, sent Hagrid to communicate with the giants. I am not sure if Madame Maxime was also in the Order, but she did go to the giants on Dumbledore's orders, when he was reinstating the Order. Hagrid also fought on Harry's side in the final battle, and he was the Real Harry's escort at the beginning of DH. Hagrid was unable to fight with the Order at the end of OotP because he was in hiding after Umbridge tried to fuoco him. Some may argue that Hagrid only went to the giants on Dumbledore's orders, outside of the Order, and some may argue that he fought on Harry's side because he was a good person and a friend of Harry's, but I think that he knew a lot about Voldemort (remember Hagrid's first descrizione of him to Harry- don't think there was enough human left in him to die) and he was loyal to Dumbledore, therefore I believe that he couldn't NOT be a member of the Order.
