late 14c., registre, "public record book, private account book, an official written account regularly kept," from Old French registre (13c.) and directly from Medieval Latin registrum, regestrum, properly regestum, from Late Latin regesta "list, matters recorded," noun use of Latin regesta, neuter plural of regestus, past participle of regerere "to record; retort," literally "to carry back, bring back" from re- "back" (see re-) + gerere "carry, bear" (see gest).
With unetymological second -r- in Medieval Latin and Old French by influence of other Latin nouns in -istrum (French -istre). The word was also borrowed in Dutch, German, Swedish, Danish.
Some later senses seem to be influenced by association with unrelated Latin regere "to rule, to guide, to keep straight." Meaning in printing, "exact alignment of presswork" is from 1680s. Musical sense is from 1811, "compass or range of a voice or instrument," hence "series of tones of the same quality" (produced by a voice or instrument).
From mid-15c. as "a record-keeper, recorder;" sense of "device by which data is automatically recorded" is by 1830, from the verb.