In the expression "j'ai hâte" "hâte" is not a verb, it's a noun (la hâte), like envie in j'ai envie de…
If you want to use the verb "hâter" you would change the meaning, for example "je me suis hâté de voir se film" = I rushed to see this movie, or j'ai hâté mes pas pour arriver plus vite (I walked quickly to arrive early)
If you want to use a verb, you could use something like "Il me tardait de voir les Misérables"…