late 14c., "a thing done," from Latin actus "a doing; a driving, impulse, a setting in motion; a part in a play," and actum "a thing done" (originally a legal term), both from agere "to set in motion, drive, drive forward," hence "to do, perform," figuratively "incite to action; keep in movement, stir up," a verb with a broad range of meaning in Latin, including "act on stage, play the part of; plead a cause at law; chase; carry off, steal;" from PIE root *ag- "to drive, draw out or forth, move."
Theatrical ("part of a play," 1510s) and legislative (early 15c.) senses of the word also were in Latin. Meaning "one of a series of performances in a variety show" is from 1890. Meaning "display of exaggerated behavior" is from 1928, extended from the theatrical sense. In the act "in the process" is from 1590s, perhaps originally from late 16c. sense of the act as "sexual intercourse." Act of God "uncontrollable natural force" recorded by 1726.
An act of God is an accident which arises from a cause which operates without interference or aid from man (1 Pars. on Cont. 635); the loss arising wherefrom cannot be guarded against by the ordinary exertions of human skill and prudence so as to prevent its effect. [William Wait, "General Principles of the Law," Albany, 1879]
To get into the act "participate" is from 1947; to get (one's) act together "organize one's (disorderly) life" is by 1976.