1660s, "reference, relation, relationship," from French rapport "bearing, yield, produce; harmony, agreement, intercourse," back-formation from rapporter "bring back; refer to," from re- "again" (see re-) + apporter "to bring," from Latin apportare "to bring," from ad "to" (see ad-) + portare "to carry" (from PIE root *per- (2) "to lead, pass over"). The Old French noun was report "pronouncement, judgment," from reporter "to tell, relate" (see report (v.)).
Especially "harmonious relation; accord or agreement; analogy." Psychological meaning "intense harmonious accord," as between therapist and patient, is first attested 1894, though the word had been used in a similar sense with reference to mesmerism from 1845 (in Poe). Also see report (n.).
Formerly often used as a French word, and in en rapport. Johnson  frowns on the word and credits its use in English to Sir William Temple, notorious naturalizer of French terms, who did use it but was not the first to do so. Fowler writes that it was "formerly common enough to be regarded and pronounced as English," but in his time  the word seemed to have reacquired its Frenchness and was thus dispensable.