According to this list, only a few news organizations accept donations in the currency: Among them, two that say they're affiliated with the hacking collective Anonymous and Juice Rap News.
Setting up the donation mechanism "was easy," inewsource reporter Brad Racino, who arranged the method, tells Poynter in an email. He used a site called Coinbase that was free but requires a verified bank account, which receives the donations in cash. "The site generates a code for a bitcoin 'button' you can place on a website. It's the same as, say, a Paypal button," Racino writes. "Donors just click the button, log into their bitcoin account, and choose an amount to donate from their digital wallet."
As of the time I'm writing this, 1 bitcoin is worth $1,056.53.
Related: I'm Changing My Mind About Bitcoin (Business Insider)