I've heard rumours but I'm not sure if they are true...

Not by a long shot.

A good bet would be for Punisher (Feb 74), who edged out Wolverine by a few scant months.

Well, antihero is kind of a broad term. There were definitely antiheroes long before comics even existed. Even in comics, they've been around for a while. The oldest I can think of is the Shadow.

Ya I would have to go with some classic golden age characters like The Shadow, The Phantom, I believe Namor was called an anti-hero back in the day as well. Lets not forget Batman can be classified as an anti-hero as well.

Rorschach being based off off Mr. A makes it kinda hard for him too be the first. Also the Comedian appears in Watchmen before Rorschach so even if Watchmen was the first appearance of the Anti-Hero Comedian would technically be the first.

Def@Nova`Prime` said:

" Ya I would have to go with some classic golden age characters like The Shadow, The Phantom, I believe Namor was called an anti-hero back in the day as well. Lets not forget Batman can be classified as an anti-hero as well. "

While a good number of pre-code characters took their anti-hero cues from film and literature, I'd have to say that the vast majority of them switched to "standard hero" post comic-code or simply went out of publishing due to the new regulations. 
 
Post code, I'd still go back to the Punisher marking the return of anti-heroes.

Nope. But Batman was one the first antiheros