Is there a way to pay my credit card balance with bitcoins? So imagine that I have 200 USD on my credit card balance from a bunch of small purchases and bar drinks and tips that I want to pay using bitcoins. 

I know that I can but gift cards from gyft or do online purchases using joinsnapcard. But If I invite a round on my local non-bitcoin-friendly bar, I want to pay with bitcoin anyways (even I I use credit card system as proxy)

Is there any service that does that for me?

Edit 2017-07-27:  There is a debit card that can be funded with Bitcoin, Ethereum and Litecoin (via Coinbase) called ShiftCard https://www.shiftpayments.com/ 

Thanks,
Nico
If you live in the states the only service that comes close to this would be

https://www.xmlgold.eu/  - you can even order a pre-paid credit card that you are able to top up with bitcoins.

https://www.okpay.com/en/index.html - Okpay used to offer the same service but due to regulatory reasons they have ceased offering thier services to US citizens.  

The only other way I can think of to do this would be to use http://bitcoin-otc.com/  here you  can see if you can find anyone willing to pay off your credit card for bitcoins.  Its kind of like online trading pit.  Hope this helps.