Jack Dorsey's company is testing support for bitcoin through its Cash payments app.
"We're exploring how Square can make this experience faster and easier, and have rolled out this feature to a small number of Cash app customers," a Square spokesperson said via email to CNBC. "We believe cryptocurrency can greatly impact the ability of individuals to participate in the global financial system and we're excited to learn more here."
The test does not allow individuals or businesses to send or accept bitcoin, Square said.
Shares of Square spiked more than 5 percent Wednesday to a record high as one Wall Street firm was quick to recommend the stock on this potential development. The stock closed up 2.3 percent at $40.66 a share.
"We believe it could place SQ in an early-mover position as a mainstream fin-tech company providing crypto-currency services," Credit Suisse analysts Paul Condra and Mrinalini Bhutoria wrote on Wednesday. "SQ is also well positioned to enable crypto transactions at the physical point of sale."
Credit Suisse has a neutral rating on the stock and maintained a price target of $31, nearly 22 percent below where Square closed Tuesday.
Buying and selling bitcoin has become a big business. Coinbase, the leading U.S. platform for such services, has 12.5 million users and says on its website it has exchanged $40 billion worth of digital currency. That means Coinbase's user growth has more than doubled from 5.5 million in January, according to analysis of public data compiled by Alistair Milne, co-founder and chief investment officer of Altana Digital Currency Fund.
Source: Alistair Milne, Coinbase
The price of bitcoin has leaped by more than seven times this year. The digital currency recovered from a sharp weekend plunge and traded more than 9 percent higher Wednesday above $7,200, according to CoinDesk.
Other stocks have surged this year following news the companies were working on bitcoin-related projects. Notably, shares of Overstock.com are up 187 percent this year as its roughly three years of work in developing businesses related to bitcoin's blockchain technology caught investors attention.
Square was tracking for gains of about 198 percent for the year as of Wednesday's close.
However, Square's test of bitcoin is still small and focused on letting customers buy and sell the digital currency within the app.
"It's nice, but I think the bigger thing is if you can eventually be able to pay with Square [point-of-sale terminals] with bitcoins," Nomura Instinet analyst Dan Dolev told CNBC. "It's a nice PR thing but it's not a fundamental mover and shaker."
Dolev has a buy rating on Square with a target price of $45 based on his view the company is increasingly disrupting the payments industry and gaining traction with larger merchants.
There are other risks for working with a digital currency that governments have watched warily.
"We believe the largest risk is regulation, which could limit its ability to provide the service or outright ban it. SQ is also exposed to liquidity and counterparty risk as it must source bitcoin for users either by pre-buying or using an exchange," the Credit Suisse analysts said. "Despite these risks, the upside could be significant if crypto currencies become more mainstream. We believe PayPal (PYPL) is also well positioned to provide such services."
PayPal and its Braintree payments platform for merchants have experimented with offering support for cryptocurrency, but merchant adoption and transaction volume were low, spokeswoman Amanda Miller said in a statement to CNBC. "If consumer demand increases for any new form of currency, we will consider support for those new payment methods as they become relevant to our customers over time."
PayPal shares closed 1.4 percent lower, holding gains of 86 percent for the year.