Pretty much, you can't - or at least, not simply.
The problem is that SQL doesn't have a date format style that includes the day of the week: SQL Server CONVERT() Function
] so you need to do some farily serious string manipulations first.
If you strip off the day of the week, it's fairly simple:
CONVERT(DATE, SUBSTRING('Sat, February 20, 2016', 6 , 999), 109)
Will do it.
But...having to do this is normally a sign that your DB design is badly flawed: you should not be storing dates in string format at all because you always get problems like this. I'd strongly suggest that the real solution is to write a quick app that converts your whole DB to use a DATETIME column instead of NVARCHAR - it'll save you a lot of grief in the future.