rhapsodomancy (n.)

"divination by means of verses," 1727, from French rhapsodomancie, from Greek rhapsodos "a rhapsodist" (see rhapsody) + -manteia (see -mancy).

There were various methods of practicing this rhapsodomancy. Sometimes they wrote several verses or sentences of a poet on so many pieces of wood, paper, or the like; shook them together in an urn; and drew out one, which was accounted the lot. Sometimes they cast dice on a table, on which verses were written; and that on which the die lodged, contained the prediction. [Rees' "Cyclopedia," London, 1819]