I think Bitfinex lends BTC to short from what Frozenlock has said. There may be others. Some online FX brokers are now offer BTC CFD's. Plus500 and Spreadex to name two accessible in the UK. I am sure there are many more. But tread carefully and manage your risk well if you intend to use leverage on something like Bitcoin. Things can blow up in your face real quick if you don't have the cash to cover it. TBH, for me the leverage just serves as a way to give them less of my fiat.
A CFD is a Contract For Difference in case you are not aware- basically a bet that the price will go up or down where you make or lose only fiat and never touch the underlying asset, though the issuer may do. Its a derivative - the paper shit that Rampion hates ! TBH for me it's not the 'paper shit' that is the issue, it is it's misuse/abuse that is the problem. Any market should have the ability to go short in my opinion otherwise there is no way for true price discovery. It's when the derivatives become greater than the value of the underlying that the problems start to arise and the house of cards starts to be built . When people use them to magnify position to such an extent that a small unexpected move can 'blow them up' that the systemic risk arises. See Long Term Capital (Mis)Management for the best example. And Lehmans for the more widely known one.

EDIT : I normally don't disclose my positions - I feel it can bring bad luck. I just felt in this instance it was necessary