Two practical approaches should work:

1. Do it physically: Put the shirt on a large pillow or other soft support, then roll a wet, dirty bike tire over it to make real marks. After that, wear the shirt and take the photo. This is the simplest way to get realistic texture and fabric interaction.

2. Composite it in Photoshop: Photograph yourself in the final pose, then separately photograph an actual tire track—such as by wetting the tire and rolling it over a clean, dry floor. Bracket exposures so you have a version with strong contrast. Then blend that tire-track image onto the shirt in post.

If you use Photoshop, a displacement map can help the track follow the shirt’s wrinkles and surface contours so it looks more natural than simply overlaying a flat texture.

In short: for maximum realism, make real tire marks on the shirt; for more control, shoot the track separately and composite it with a displacement map.