Is it ethical to force a draw via perpetual check? I was playing this game. I was white. We reached a point where my opponent could checkmate me in one move (by moving Rook to C1) but I forced him to a draw by stating that I would constantly check him to all eternity using my two rooks. 

He agreed to a draw but after a while it didn't feel right to me. I regretted forcing him to draw, I felt it was cheap of me to do so, and I think that he deserved a win. 

So my question is: Is it ethical to force a draw like this one?
There is a rules in chess called Threefold repetition rule. This rule states that you can claim a draw if you are about to repeat the the position for a third time. This subsumes a situation called perpetual check which also leads to a draw.

So what you did in your game wasn't a case of extortion or abusing a flaw in the game - it was completely by the rules and everyday thousands of games are drawn in exactly that fashion. 

PS: You also could have stopped the mating threat by playing Rc7, this would have given you a winning position as far as I can see. So by resigning you actually would have turned a winning position into a loss.