Correspond, write a short letter or note. For example, I hope you'll drop me a line soon. This idiom uses line in the sense of “a few words in writing,” a usage first recorded in 1647.
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.