If you're not employed in the US by it or receiving payment from it in the US (except a dividend) then I can't see why not. Essentially you're just a shareholder. And I can't see why you couldn't be a director if you receive no renumeration in the US. Plenty of US corporations with celebrity foreign directors on the board for show.
Like I said, there's no real difference between that and going to a stockbroker and buying some stock in a corporation.
There may be catches in the corporation law because you're a non-resident director and the corporation is essentially foreign-owned, which may mean you have to pay higher corporation taxes or form your corporation in a certain way. For example you could not use an S-corporation which is how most small corporations in the US are formed. This means you have to use one of the more conventional forms of corporation. Have a read of this:
http://www.window.state.tx.us/taxes/ these are the State taxes on corporations.
Federal taxes on conventional corporations in the US are higher than they are in Canada, and significantly higher than they are on CCPCs.
So yes, possible, but tricky and you will almost certainly pay higher taxes than an American would.
Steve.