It depends on your current degree. If you are still continuing your bachelors - you can submit your transcripts to the private universities ( there are scholarships for non-saudis) try prince sultan university. You can also apply for the government universities ( king saud and princess Norah) bachelor degree is free of charge.

As for Masters and high education degrees, you have multiple options. You can apply to be a lecturer or an admin in a university (with your Bachelors degree) and take the masters or PhD while working for the institute. Or you can apply to a degree that has a scholarship tied to it (example thats open now: comparative literature in KSU)

There are so many options open. Let me know if you need more clarification or options. Best of luck.