Most insurance companies offer insurance for six or twelve month terms, but you don't have to pay it in full at inception. You typically make a down payment then make payments. Each states have requirements on the minimum down payment, but it is typically 25% of the policy premium. At CarInsurance.com you can purchase insurance for 6 months or 12 month terms, but you have the option to cancel your policy when you don't need the insurance anymore. Some state laws may restrict you to maintain the policy for at least 60 days without reason to cancel.
You can purchase insurance for the shortest term offered and request that it be cancelled after one month. In most cases, you will need to make this request in writing. It is also possible that you will need to provide additional information and may be subject to an early cancellation fee if you cancel mid term. Some states have pro-rate cancellation refunding setup.
Some states with mandatory insurance laws require proof of other coverage or proof that there is no insurable interest (you sold the car, moved it out of state, destroyed it, etc.), in order to cancel within a certain amount of time (typically 60 days).
We are happy to sell you a car policy and to accommodate your needs.
Comment Update: There is not a specific company or site that offers one month policies. Typically, the shortest term is 6 months, but you have the opportunity to cancel the policy. We don't currently offer one month policies in any states, but some of our out-of-site partners may offer them.