The comments came in the wake of the publication of a recording in which he made obscene remarks, which sparked a string of sexual assault claims.
Polls suggest Mr Trump is losing ground in some of the key battleground states.
Speaking at a rally in New Hampshire, Mr Trump said Mrs Clinton had been "all pumped up" at the beginning of the last debate but could "barely reach her car" at the end.
"We should take a drugs test," he said.
He did not provide any evidence to back up his claim.
More about:
