A medication that's used to relax patients is called a tranquilizer. If someone suffers from severe anxiety, their doctor might prescribe a tranquilizer.
The word tranquilizer is commonly used for anti-anxiety or anti-psychotic drugs, but it's not the term most medical professionals use. They are much more likely to use sedative, neuroleptic, or anxiolytic for a calming medication. Tranquilizer, from tranquility or "the state of being calm," was first used for sedatives in 1824, and for anti-anxiety drugs in 1954.