It's just as likely tape tension as alignment. There's a tension band and arm that keep the tape tight around the drum, it could be that. Unless you know what you're doing, you can do more harm than good trying to align. The 2 tape guide rollers do alignment. Make sure both guides are locked in place before messing with the guide rollers. If they don't lock in place, that's the problem.
It may also be something as simple as a need for cleaning. If the capstan is gunked up bad enough, it will not allow a straight and true travel of the tape through the path.
Another possibility: bad cassette. This can be confirmed if the unit plays other tapes properly. - Reinhart