Christians can not be possessed by demons, but we are told not to yield "our members" unto unrighteousness.
Rom 6:13 Neither yield ye your members as instruments of unrighteousness unto sin: but yield yourselves unto God, as those that are alive from the dead, and your members as instruments of righteousness unto God.
Rom 6:14 For sin shall not have dominion over you: for ye are not under the law, but under grace.
I have no doubt whatsoever that Christians can be possessed.
There are countless cases of possession of Christians, incl. great saints.
One famous case was Anneliese Michel, a devout Christian that was possessed and killed by several demons. According to the exorcists, God didn't allow her to be delivered, so that her suffering could be used to save many souls.