I have a friend who has transfered a Cross Orbweaver spider [Araneus diadematus] into her house as a pet.
The site http://www.spiders.us/species/araneus-diadematus/ has details on this species. Since this common species is easily found in gardens or grassy areas, not dangerous to humans, and stays put in one location once it has built a web, it might be what you are looking for. The spider seems to be happy building her web inside in semi-shaded upper corners of window frames. A window with a tall plant might make it more attractive to the spider. Except for the occasional misting of the web with water, they take almost no care at all.
Once you locate the spider's web, determine the location of the webs three anchor points. Break the bottom anchor. The spider will start gathering the web material. When she has most of the material gathered into a ball, break both upper web anchors and use one of the anchors to lower the spider into a container with a lid and then close it. Now move the container into your house to the window you wish her to live in, open the container, and leave her alone to climb out and select her new web location. These spiders do not normally live longer than a year or so, since they normally lay eggs and then die over the winter.
Update: My friend kept her spider for four years, so apparently these spiders can last multiple years under optimal conditions (like not having to live through freezing temperatures outside).