This is a non-native species to North America (they can be found in the southern US and have become somewhat invasive in areas). You should be able to find some information online on care for anoles. Some people do keep them as pets.
Here are a few I found on a quick search for "Brown Anole care" on Google:
http://www.reptilesncritters.com/care-guide-brown-anole.php
http://whitepython.com/reptile-care/brown-anole-lizard/
http://www.the-lizard-lounge.com/content/species/brown-anole.asp
I do not know which is the best advice, but it is somewhere to begin. You can also check for local reptile rescues in your area. They may have good information of care for this small lizard. Good luck!
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