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No, that would be a violation of their rights to privacy. So you couldn't force a tenant to submit to a drug test. However, a landlord could refuse to renew their lease when it expired if they wouldn't submit to one or could choose to terminate their lease if they were month to month with proper notice if they refused to agree.
So the landlord couldn't directly force a tenant to agree, but could indirectly do so by agreeing or refusing to continue the tenancy if they didn't comply.
As an aside, in addition to being an attorney, I have also been a landlord for over 26 years...