Yes, as long as that individual is not under a court ordered guardianship which specifically prohibits voting.
Any patient in a nursing home must be a registered voter in order to vote by absentee ballot and must fill out an absentee ballot application.
If the clerk designates a health care facility in writing 28 days before the election, the ballot must be hand-delivered to such facility by a Registrar. If the patient states that he/she has entered a hospital after noon of the fifth day before the election, the ballot may be hand-delivered to the voter; otherwise, the ballot should be mailed to the voter at the facility.
Consult the administration of the nursing home for further instructions.