by 1914 as "to subject to psychoanalysis," short for psychoanalyze. From 1934 as "to outsmart" (also psych out), and by 1952 in bridge as "make a bid meant to deceive an opponent." From 1963 as "to unnerve." However to psych (oneself) up is from 1972; to be psyched up "stimulate (oneself), prepare mentally for a special effort" is attested from 1968.
short for psychology in various senses; e.g. as an academic study, in student slang by 1895.