"cross-tempered, irritable," 1807, from crank (n.) + -y (2). The evolution would be from earlier senses of crank, such as "a twist or fanciful turn of speech" (1590s); "inaccessible hole or crevice" (1560s). Grose's 1787 "Provincial Glossary" has "Cranky. Ailing sickly from the dutch crank, sick," and identifies it as a Northern word (this is probably from the vagabond slang sense, which ultimately is from German krank "sick"). Jamieson's Scottish dictionary (1825) has crank in a secondary sense of "hard, difficult," as in crank word, "a word hard to be understood;" crank job, "a work attended with difficulty, or requiring ingenuity in the execution." Related: Crankily; crankiness.
Ben. Dang it, don't you spare him--A cross grain'd cranky toad as ever crawl'd. (etc.) [Richard Cumberland, "Lovers Resolutions," Act I, 1813]