The US social media giant, which did not disclose details of the deal, will take over the staff and offices of the firm, which is based in the southern Indian tech city of Bangalore.
"Our primary mission, bolstered by this acquisition, is to help every Indian with a mobile device get a great, relevant Twitter experience," wrote Twitter's India marketing director Mr Rishi Jaitly in an official blog.
ZipDial's chief executive Ms Valerie Wagoner applauded the deal as a "huge achievement", adding that the company had come a long way since starting in 2010.
ZipDial gives clients phone numbers for use in marketing campaigns. Clients call the numbers and hang up before being connected, incurring a charge, and then receive a phone call or text message from a company receiving free promotional material.
"We will continue building upon the existing ZipDial platform, and now, by coming together with Twitter, we have the tremendous opportunity to elevate everything we have built to a global scale," Wagoner said in a statement.
Financial terms were not disclosed, but local media reported the deal at US$30 to $40 million.
India's mobile base is expected to rise sharply in coming years from the current 900 million-plus connections as huge numbers of young people come online and enter the workforce.
"With the Cricket World Cup around the corner, the rise of Twitter as a tool for governance, and more Indian icons joining our platform everyday, 2015 promises to be another big year for Twitter in India, one of our fastest-growing countries worldwide," Mr Jaitly said.
The deal is the latest by global tech giants who have bought startups in India. Facebook bought Bangalore-based mobile technology firm Little Eye Labs last year to help the social network develop performance analysis and monitoring tools.
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