1
general::
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.
American Heritage Idioms
2
general::
Phrase(s): drop someone a line [and] drop someone a few lines; drop someone a note
to write a letter or a note to someone. (The line refers to lines of writing.) • I dropped Aunt Jane a line last Thanksgiving. • She usually drops me a few lines around the first of the year. • Drop me a note when you get a chance.
McGrawhill's American Idioms And Phrasal Verbs