Terms weren't disclosed, but a person familiar with the matter said the cost was nearly $200 million..
Shares of PayPal, San Jose, Calif., at last check were down 3.7% at $230.10.
PayPal said in a statement that Curv would become part of its recently created business unit that focuses on blockchain, cryptocurrency and digital currencies.
"The acquisition of Curv is part of our effort to invest in the talent and technology to realize our vision for a more inclusive financial system," Jose Fernandez da Ponte, PayPal's vice president and general manager for blockchain, crypto and digital currencies, said in a statement.
PayPal said it expected to complete the acquisition in the first half.
In February, PayPal beat Wall Street's fourth-quarter estimates due to the high demand for its payment services that was sparked by the COVID-19 pandemic.
In the quarter the company’s net new active accounts soared 72% from a year earlier to 16 million.
Last year, PayPal said that all eligible PayPal account holders in the U.S. could buy, hold and sell cryptocurrency directly through its network.
The company said last month that it would bring cryptocurrency trading to its popular Venmo app within months.
Curv was founded in 2018 by Chief Executive Itay Malinger and Chief Technology Officer Dan Yadlin.
Curv says on its website that its "expertise in cryptography and cloud security allowed us to create a secure, distributed architecture for signing transactions.
"This allows any institution or enterprise to quickly and easily hold and exchange digital assets on public or private blockchains without managing private keys on outdated physical infrastructures."