Can a cut on your head cause dizziness?

Indirectly: If the cut results in sudden loss of blood it can. Severe associated pain may cause an autonomic reaction resulting in dizziness. If a person is of an emotional, anxious nature dizziness may be a common reaction pattern.

Yes: Cuts on the head, even fairly minor ones can bleed significantly. Dizziness can be due to excessive bleeding, a vagal response (often a lightheaded feeling), or from an underlying brain injury. It all depends on the size of the cut and the nature of the injury. If this persists i would certainly seek medical attention.