Yes, you can purchase long-term care insurance coverage from a handful of different providers, but its value is questionable. The premiums are quite high if you obtain the coverage when you are a senior citizen, and the rates can go up after you start carrying the insurance.
There is also a waiting period, so the coverage does not kick in as soon as you need long-term care. Depending on the policy, it will usually be 60 days or 90 days, so you have to pay out-of-pocket during this interim. Many people would say this defeats the purpose of the insurance.