A pinky promise (or "pinky swear") is a gesture in which two parties interlock little fingers in a symbolic gesture of agreement. What is the origin of this phrase?
One possibility, and probably the most straightforward one, is that it is an independent invention to describe an existing cultural practice of sealing promises by interlocking little fingers.
Another possibility, however, is that it originates from Japanese. Japanese sources frequently suggest that the English phrase "pinky promise" is a translation/adaptation of a similar Japanese concept called 指切り (yubikiri, lit. "finger-cutting") which supposedly has its origins in yakuza loyalty practices (if someone promised to do something and performed a yubikiri, and then broke their promise, their finger would be cut off).
However, as Wikipedia notes, this practice (if not the exact phrase "pinky promise") has been attested since 1860, as recorded in Bartlett's Dictionary of Americanisms. The Japanese yubikiri predates that1, so it's still possible that "pinky promise" derives from yubikiri, but I can't imagine there were many borrowings/translations from Japanese that long ago.
1 The Nihon Kokugo Daijiten, which is closest thing Japanese has to the OED, attests yubikiri in the sense of "a promise" from 1638, and in the sense of "cutting off a finger" from 1692.