Can I rent out a property I do not own?

[Priscilla Wong]

I am helping my parents move from their house to a condo that we helped buy with them last year. My husband and I are thinking whether we should fix up their old house to rent it out (the house is free and clear estimated around +$600k with market rents in the neighborhood of $2500/month), but it needs work (cracked walls, replace carpet, remodel kitchen/bathrooms). 

I am interested in renting out the house after remodeling, but we live 300 miles from the house, and my parents are getting older and do not want to deal with the headache of renting it out, so they are giving us the option to do what we want with it. I was thinking...can I rent it out and collect the rental income for this house if I do not own it? We probably would want to give my parents some money monthly, but am I allowed to put it on my schedule E in order to deduct different expenses?