commit to memory
Learn by heart, memorize, as in The director insisted that the altos commit their part to memory by Tuesday. First recorded in 1875, this phrase today is often replaced by the shorter memorize.
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.