This is a strategy that is currently being tested. The concept of giving antibodies from one person to another to protect from disease is called passive immunization. You may also hear about this in the context of convalescent serum; serum just refers to the part of the blood that has antibodies in it.
The National Institutes of Health COVID-19 Treatment Guidelines do not recommend either for or against the use of COVID-19 convalescent plasma for the treatment of COVID-19, citing "insufficient data from well-controlled, adequately powered, randomized clinical trials to evaluate the efficacy and safety of convalescent plasma for the treatment of COVID-19."
Updated 20 October 2020