2,179,931 games on average every 24 hours
I would assume an average of 50 kills per game
Its been out for around 7 months which is about 210 days.
~22,889,275,500 kills
Keep in mind this is a rough estimate using a daily average 7 months after release.
"Do they have a counter for online though? I'm sure it's over 20 billion or something. =P"
Pretty good guess you made there.