You can usually get rid of and kill a rat in your house by using some rat poison set out but when you do use rat poison then the rat will die eventually and likely cause a stink in the house until you find it.
Another option is to set out a live trap with some bait such as peanut butter, bread, vegetables, fruits, bacon or other meats to catch the rat live and then don't release it but just let it die in the live rat trap outside or if you have a gun then shoot the rat.
Those rats shouldn't be released live since they can come back into your home and spread diseases in your home as well as other peoples homes.