The price of Bitcoin surpassed $1,000 again on the Mt.Gox exchange, after Zynga Inc. said it would start accepting the virtual currency for some of its online social games as the digital money becomes more widely used.

Bitcoins, which exist as software and aren’t controlled by any country or banking authority, surged to about $1,119 on the exchange Sunday, one of several markets where they are traded for dollars, euros and other currencies.

Bitcoins first crossed the $1,000 threshold in late November and reached record at $1,238 on Mt.Gox on Dec. 4, but then plummeted to as low as $640 after China’s largest online market for the virtual currency stopped accepting deposits. The digital currency has rebounded as more merchants accept Bitcoins for everything from Gummi bears to smartphones on the Internet. Zynga is the latest merchant to accept Bitcoins, which can be used to buy virtual items in games.

“Bitcoin has been remarkably resilient in the face of all the bad news out of China,” Nicholas Colas, chief market strategist at ConvergEx Group, wrote in an e-mail. “The strength shows a continued interest, which is a very positive sign.”

Bitcoin was trading for about $13 a year ago, before wider acceptance and speculators drove prices higher. The rally gained steam in October, after regulators shut down the Silk Road Hidden Website, where people could obtain guns, drugs and other illicit goods using Bitcoins. That generated optimism the digital money would become more widely used. In November, law enforcement and securities agencies said in U.S. Senate hearings that Bitcoin could be a legitimate means of exchange.

Bitcoin Shopping

Dani Dudeck, a spokeswoman for San Francisco-based Zynga, confirmed a post introducing a plan to test Bitcoin payments by the company on the reddit.com community website. Players will be able to pay via the BitPay payments service for players of FarmVille 2, CastleVille and other games, Zynga said.

“We look forward to hearing from our players about the Bitcoin test so we can continue in our efforts to provide the best possible gaming experience,” Zynga said.

Victoria’s Secret Stores LLC has signed up with Gyft, an app that lets users buy gift cards with Bitcoins. Overstock.com Inc. plans to start accepting Bitcoins next summer, Chief Executive Officer Patrick Byrne said in an interview last month.

“We think there’s an underserved part of the market that wants to use Bitcoins and can’t,” Byrne said. The company needs time before it starts accepting Bitcoins in order to figure out how to process Bitcoin transactions and to hedge Bitcoin sales (the currency is highly volatile), he said.

Digital Money

Introduced in 2008 by a programmer or group of programmers going under the name of Satoshi Nakamoto, Bitcoins exist as software, which contain the rules governing their supply. New Bitcoins can only be created by solving complex problems embedded in the currency, keeping total growth limited. There are more than 12 million Bitcoins in circulation, according to Bitcoincharts, a website that tracks activity across various exchanges.

The virtual currency can also be traded without being tracked, potentially reducing banking-transaction fees and making it an attractive tender for those seeking to buy and sell via the Web or in stores.

“I think that as demand for investing in Bitcoin rises and friction in its markets is removed the price will continue to go up,” Gil Luria, an analyst at Wedbush Securities Inc., said in an e-mail. “The $1,000 mark does seem to be important level because it may dissuade the skeptics that emerged when Bitcoin prices took a big step down.”