Short answer: a rebuilt one, usually yes. A salvage one, generally not until it's rebuilt.
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Insurers treat these as two different things, and most confusion about "salvage title insurance" comes from mixing them up. A car on an active salvage title generally can't be registered or driven on public roads, so there's nothing to insure in the ordinary sense. Some insurers will write storage or comprehensive-only cover while it sits, but you won't get road cover for a car that isn't road-legal. A rebuilt title car has been repaired and has passed a state inspection, so it's registered and road-legal. That one is insurable, and most drivers of rebuilt cars carry ordinary policies.
Liability cover -- the part that pays for damage you cause to other people -- is usually straightforward on a rebuilt car. It's priced on you and your driving, not on the resale value of your vehicle, so the title brand barely matters. Comprehensive and collision are where you'll meet resistance. Those pay out based on what your car is worth, and an insurer's problem is that a rebuilt car's value is genuinely hard to pin down and its repair history is hard to verify. Some carriers decline it outright, some write it at a reduced valuation, and some will do it if you can document the repair.
It isn't arbitrary. From the insurer's side, a previously totalled car carries two real unknowns: whether the structural repair was done properly, and what the car is actually worth today. If they later have to settle a claim, both questions become expensive arguments. Declining is simply cheaper than resolving that case by case. This is also why carriers differ so much. Large national insurers tend to have blanket rules; smaller regional carriers and independent agents are more often willing to look at the individual car. It's worth calling more than one.
Documentation, and specifically documentation about the repair rather than the damage. The state rebuilt inspection certificate is the strongest single item -- it's an independent party saying the car was checked. Repair receipts for parts and labour, an alignment printout, and photos of the car during the repair all help for the same reason: they turn "previously totalled" into a known quantity. An independent appraisal is worth getting if you want full coverage on something valuable. It gives the insurer a number to write the policy against instead of guessing.
Liability on a rebuilt car is typically priced much like any comparable vehicle. Where you'll feel the brand is in what a comprehensive or collision claim pays out: settlements on rebuilt cars are generally based on a reduced value compared with a clean-title equivalent, because that's what the car is worth. That's worth thinking through before you buy full coverage at all. If the car is worth a few thousand dollars, paying for collision cover that would settle at a reduced value may not be money well spent -- liability plus savings can be the better arrangement. Insurers vary enormously on all of this, so treat quotes as the only real answer.
Sometimes, and it depends heavily on the carrier. Liability is usually easy; comprehensive and collision are where carriers differ -- some decline, some write it at a reduced valuation, and some will cover it if you can produce the rebuilt inspection certificate and repair documentation. Call several insurers rather than assuming the first no is final.