Yes, it is possible to buy a life insurance policy naming your brother as the insured, and yourself as the beneficiary. You would be the owner, and responsible for paying the premiums on the life insurance.
In order to buy life insurance on another person there must exist an Insurable Interest in that person. This means, you may stand to lose financially if the person were to die, or you rely on that person for some means of financial support.
Insurable Interest does exist between spouses, parents and their children, siblings, relatives, business partners, etc.
However, in order to buy life insurance on someone else, you also need that person's permission/approval, signature on the application, and the person may have to answer some health questions, and/or take a paramedical exam in order to qualify for the life insurance coverage.
Learn how you may apply for term life insurance online.