“Twitter does not block Tor, and many Twitter users rely on the Tor network for the important privacy and security it provides,” Twitter spokesperson Nu Wexler told Motherboard in an email. “Occasionally, signups and logins may be asked to phone verify if they exhibit spam-like behavior. This is applicable to all IPs and not just Tor IPs.”
It also might not actually be necessary to provide a phone number to regain access. The coder known as stribika recently noted they got back in after messaging Twitter Support.
This certainly isn't the first time that Tor usage has clashed with popular services. Last year, a blog post from the Tor Project pointed out that plenty of sites make it difficult for users to connect or enjoy full functionality over a Tor connection, and this reporter temporarily had his Gmail account locked down for using the anonymity network.
That situation with Google was very similar to this Twitter one: Google asked for a phone number to send a verification code to. And again in that case, the account wasn't targeted specifically because it was using Tor, but rather that the email service's security system detected what it felt was suspicious behavior.
It's a tricky problem to solve: how does Twitter separate spam-looking activity from legitimate privacy centric users?