You should be able to get a better rate but why did they ratejack you and who are they? Chase? HHB? If your utilization remained at over fifty percent of thel imit for some time, cards are known to ratejack. If you've opened a lot of new credit lately, they may ratejack you just on the assumption that if you max it all out you won't be able to repay. Have you called them to ask them to lower it?
By all means when a card ratejacks you like that they are telling you in credit-ese that they do not want your business especially if they refuse to lower it.. Don't close the card just get a new one, keep utili low and keep that card in your sockdrawer breaking it out every 4 mos or so for a pack of gum. Eventually they will ask nicely that you begin using the card again by lowering your interest rate but hold out for a better deal than you initially had