You can bring the cat indoors and put it in your bathroom. Put signs up on phone poles saying: FOUND CAT/PHONE.
Place an ad on Craigslist, as well, with a picture. Look at the Lost ads.
No, it is not common for a cat to do this. Either someone dumped it and it is waiting for them to return, or it is simply lost and doesn't know what to do. The cat obviously wants you to help it, so bring it inside and place in your bathroom. DO NOT take it to an animal shelter, because they put 80% of cats down in shelters, no matter what they tell you.
We once found a cat who had been dumped at a daycare facility. It had been placed in the fenced area, and sat there for hours, watching for its owners to return. She even became sunburned at the base of her ears, where there is scant fur. We found her a good home.
Be sure this cat doesn't have a home before finding her a home, but it is likely she is hoping your will keep her as your own.