This is exactly how we were adopted by our 2 cats!
One was mieowing at the front door, I opened it and it calmly walked in and sat on the sofa next to my husband - cutting a long story short, we still have him he is 20 years old now and we have had him for 9 years.
Flo our latest arrival (have had her for about 6 months now) did exactly like your one did tonight, wandered into the house, and then left, we occasionally saw her chasing birds in the garden, and one day she actually ate the whole bird, our friend a vet said she was obviously starving, so I started to put food out for her and eventually she became our cat, we did advertise for her owner, checked all vets/cats protection but she was obviously a stray...she is now about one year old and absolutely beautiful although very small still.
Where we used to live a neighbours cat used to go from house to house, eating and sleeping wherever he fancied and it worked very well for many years until he passed away.
If he does come back , let us all know what you decide to do :-)