While only premium subscribers can make calls at present, all accounts can receive them, X said on its website late on Wednesday.
The feature is now available on Apple's iOS and will soon be available on Android, the company said.
Users can control who can call them through the direct messages settings. To call another user, they must have sent you a direct message at least once before, X said.
Following the policy update, Mr Musk announced that X users would be able to make video and voice calls through the platform on both iOS and Android operating systems without sharing their phone numbers.
“X is the effective global address book … that set of factors is unique,” Mr Musk said at the time.
With its latest move, the platform takes on other established apps that offer the same feature, most notably those from Meta Platforms, which include Facebook, Instagram and WhatsApp.
Mr Musk completed his $44 billion acquisition of the San Francisco-based microblogging platform last October and has made a series of changes since.
The changes are part of efforts aimed at boosting user experience and diversifying the company's revenue sources, according to Mr Musk.
He rebranded the platform to X in July in a move that reportedly wiped out between $4 billion and $20 billion in value, according to analysts and brand agencies.
In December, Twitter also relaunched Twitter Blue, the platform's top-tier account, which indicates that a user is verified, as a paid subscription service.
The premium feature’s fees start at $8 a month for individuals, with joiners getting subscriber-only features including Edit Tweet, 1080p video uploads, reader mode, the coveted blue check mark and longer tweets.
The costs of keeping the ticks start at $1,000 a month for organisations, plus $50 monthly for each affiliate or employee account.
The social media platform now also requires users to have an account and be logged in to view user profiles and tweets, a move Mr Musk claims will prevent data from being “pillaged so much”.