I would say "he has THE reputation of being honest" or "he has a reputation FOR being honest" http://www.oxfordlearnersdictionaries.com/definition/english/reputation

The first sentence is definitely correct; "to have a reputation for" sounds the most natural, and is the construct all 3 of my grammars offer. The second sentence doesn't sound wrong either and I see it used a lot. I myself prefer "for" when a verb follows. You could also say "He has a reputation as an honest man." Using "as" requires a noun after it. I wouldn't say "he has the reputation...", but I see that also quite commonly, and it doesn't sound wrong. When in doubt about something like that, and if official grammars are silent, I try a "Google Fight": type both expressions into Google separately and see how many hits I get for them. If option A gets millions, and option B only a few, then option B is definitely wrong. If A gets millions and B gets a couple hundred thousands, then both are in use, but A is more common. Sometimes I dig a little deeper then to see whether there is some regional difference in usage.