If I was in an accident and the insurer for the at-fault driver for wants to total my car but the damage is minor, can I keep it?

You are under NO obligation to accept the settlement offer from the at-fault party's insurance carrier. 

You can reject the settlement offer, keep your car, and sue the at-fault party for negligence.  Your damages (the amount of compensation you are seeking in your lawsuit) would be the cost of repairs to your car.  Your damages should also include the cost of a rental car (if you need a rental car) while your car is being repaired.  You will need to mitigate (minimize) damages by selecting a rental car with a reasonable rate.  If you were to select the most expensive rental car you could find, you have failed to mitigate damages and your damages will be reduced accordingly.

Depending on the cost of repairs to your car, you may be able to file your lawsuit in Small Claims Court.  Your damages should also include court costs such as the court filing fee and process server fee.

You can refuse to take their offer and keep the car, but then you don't get the money. Their offer of settlement has to be voluntary on both parts: you have to agree to take it; but they can't be forced to offer anything other than what they want (e.g. money in exchange for totalling the car). You could refuse the offer and try to sue for damages (compensation), but if it turns out that the car cannot be repaired for less than it's then current value, then even in the lawsuit, you'd have to give up the car at the end (if you won) to get the money (you only can keep the car if it can be economically repaired--i.e. repaired for less than its current value): if the car is more expensive to fix now than its current value, totalling it is the correct decision.