Are employers required to pay the employee for this time he/she is on-call?

What you're talking about here is "on-call" time.  Under wage and hour law, "on-call" time must be paid by the employer only if it is "hours worked" under the law.  Whether your "on-call" time is "hours worked" depends on the facts, but generally we can say that if the employee is allowed to be at home (or away from the employer's workplace) and is permitted to use his/her time for personal matters, the "on-call" time is NOT "hours worked" for purposes of wage and hour law.  On the other hand, if the employee is required to stay on the employer's premises while "on-call" or is contacted so frequently while "on-call" that he or she cannot attend to personal business (even if the employee is permitted to be away from the workplace), then the "on-call" time may be counted as "hours worked."  Based on what information you have provided, I understand you would be permitted to be at home while "on call," and could use the time for personal business or sleeping.  I also understand you would only occasionally be called in.  Under those circumstances, I doubt the time you are "on call" would be considered as "time worked" under federal wage and hour law.  Your state law could be different, so I recommend you check with your state Department of Labor.