Here are a few past posts I made on this topic:
These all vary in terms of what they consider to be socially responsible. For example, it's pretty tough to completely avoid oil and gas companies, but the Vanguard FTSE Social Index Fund does have less than half the oil and gas that's in the US Total Stock Market (4.2% instead of 9.4%).
From a financial standpoint, I can't really recommend any socially responsible funds except for the Vanguard one because of high fees or poor performance. Here's the full list of funds that I've pulled together over time with expense ratio and ticker symbols included:
They're ordered from best to worst, more or less.
Cheers.