I doubt it would trip the sensor in the smoke detector. I have one in my bedroom and incense has never set it off before, even with the door shut and multiple incense burning at once, haha. If possible, do you have a window that can be cracked open? Or is there a way for you to pop the battery out of the smoke detector? I mean I don't advise taking the battery out for long periods of time, but if you only do it when you burn incense, and then put it back after, it should be okay.
But if you really don't want to break the rules, maybe you could use one of those wall plug-in scent things like some other people have suggested. Or get an oil diffuser, where it electrically heats the bowl and you melt scented wax or oils in it to give off the smell. Then turn it off and the oil cools, or the melted wax re-solidifies.
i would suggest candles too, I have some in my dorm room. If your RA is really picky about the rules just hide the candle when you aren't burning it. but if you really want to use the incense, do what the potheads do. take some painters (blue) tape and tape a plastic grocery bag or two over the smoke detector and seal it. I don't smoke but I have some friends who do this and it hasn't ever let the alarm go off, even with 10 or so people smoking for hours on end, up to 3 lit blunts in the room at a time. after the smell of incense has died down, just take the bag off. hope this helps!