As long as you don't sign anything that would make you financially responsible. First of all, you need a doctor's recommendation that this person go to a nursing home. You can't just sign them in.
I was able to sign for my elderly Mom being her Power of Attorney when she had to move into long-term-care. The facility made sure I signed everything with my name and placing that I was POA for "Freqflyer Mom". Some facilities aren't that careful when it comes to signatures and POA's.