If the dates are stored as strings—you say they aren't, although it looks like they are—you might use dateutil's parser:
>>> from dateutil.parser import parse
>>> from pprint import pprint
>>> bd = ['February 6, 1976','January 13, 1996','January 1, 1983']
>>> bd = [parse(i) for i in bd]
>>> pprint(bd)
[datetime.datetime(1976, 2, 6, 0, 0),
datetime.datetime(1996, 1, 13, 0, 0),
datetime.datetime(1983, 1, 1, 0, 0)]
>>> bd.sort(key = lambda d: (d.month, d.day)) # from sth's answer
>>> pprint(bd)
[datetime.datetime(1983, 1, 1, 0, 0),
datetime.datetime(1996, 1, 13, 0, 0),
datetime.datetime(1976, 2, 6, 0, 0)]
If your dates are in different formats, you might give fuzzy parsing a shot:
>>> bd = [parse(i,fuzzy=True) for i in bd] # replace line 4 above with this line