The game may have defaulted to binding the throttle on your joystick as your roll. Which joystick are you using? Is the game X-Wing Alliance?

First:
which joystick?
Second:
which operating system are you using?
Third:
Which game in the series?
Fourth:
is it literally turning or rolling?

If your stick has more than two, three or four axes, you might need to see if there is a proprietary software or some control panel in the drivers to disable the axes you won't be able to use with the game anyway.

It's also possible, like @ZyloxDragon said, that the game detected the axes out of order and you are rolling with the throttle slider instead of whatever rudder axis your stick has.

I have the exact same problem, only it's not restricted to the joystick. When I'm just trying to make a minor adjustment, the ship seems to gravitate away from targets. I tried instead to focus on a star and it didn't have any problems. I tried multiple times against still or moving targets, joystick or trackpad... there's often some level of drift when I try and focus on a target.

It's really quite annoying.