No, rental income is not subject to FICA unless the rental is a business.
The rental would be classified as a business if you provide other services - for instance, you provide regular room-cleaning service, or meals, similar to a hotel or B&B. Under those circumstances, this would qualify as a business subject to FICA.
Rental would also qualify as a business if you do it to earn a profit and you do it regularly, systematically and continuously. This definition applies even if you hire a manager to handle the day-to-day details.
This
article provides more examples of what constitutes a rental business.
In your particular situation, if you own a large office building that has many tenants, and you are renting to your partnership as one of many tenants, then you would be in the business of rentals, and subject to FICA. If, on the other hand, you own this one small building, you could argue that you are not in the business of renting.
As for whether you should increase the rent, the Fair Market Value of the space is the primary consideration. If you are renting at FMV, then the rental price you are charging is appropriate. Otherwise, the issue of profit motive may push you into the business category for this rental.
