If someone hits my car and I don’t have any insurance, can I take that person to small claims court?

Since you were not at fault in the accident, the fact that you didn't have insurance does not prevent you from filing a claim for your property damage with the at-fault party's auto insurance carrier.  This would be easier for you to get your car repaired instead of going to Small Claims Court.  If you go to Small Claims Court and get a judgment against the at-fault party, you will still need to enforce the judgment if the at-fault party doesn't pay.

If the case is settled with the at-fault party's insurance carrier, NO lawsuit is filed.

If the case is NOT settled with the insurance company, you will need to file  your lawsuit for negligence against the at-fault party/registered owner (if the registered owner is someone other than the at-fault driver).  Your damages (the amount you are seeking to recover in your lawsuit) would be the cost of repairs to your car and the cost of a rental car if necessary, while your car is being repaired.  Your damages should also include court costs which are the court filing fee and process server fee.

You will need to mitigate (minimize) damages by selecting an auto body shop whose charges are comparable to other auto body shops in the area.  If you were to select the most expensive auto body shop you could find, your damages would be reduced accordingly.  You also need to mitigate damages when selecting a rental car by selecting one with reasonable rates compared to other rental agencies in the area.  If you were to select a very expensive rental, your damages would be reduced accordingly.