Absolutely it can have an accretion disk! The disk forms because the infalling matter has some of its own angular momentum with respect to the black hole center. As the distance to the center becomes very small, the angular speed must drastically increase. So even a slight amount of drift velocity the matter had prior to falling will be amplified into a very large angular speed as it falls – this is why a vortex forms near a drain even if the quiescent bath water itself does not seem to have a strong overall rotation.
This is why a non-rotating black hole is practically impossible to create in real life. The star that it formed from will have some rotation, because the diffuse cloud of matter it formed from had an overall angular momentum about its center, and this angular momentum cannot change.
Even if a black hole somehow formed with zero spin, it would start to gain angular momentum from the matter falling into it, and end up spinning. But the accretion disk is not caused by the black hole's spin. It is better to say they are both caused for a separate reason – the behavior of matter moving in 3D space.