Twitter seems to have a complicated history with Tor's users. The linked article seems to doubt of Twitter explaining they do not put any specific restriction against Tor's IP:
Twitter does not block or force Tor users to phone verify in order to
sign up. Occasionally, signups and logins may be asked to phone verify
as they may exhibit behavior similar to spam. This is applicable to
all IPs and not just Tor IPs.
However, chances are that such restriction are effectively caused by a side-effect of using Tor. Indeed, when using Tor you share the same IP address pool than all the other users, including malicious ones. Twitter servers have no way to ensure that the request coming from an IP which was once used by a spammer now comes from a legit user.
That's why, while Tor may indeed not be specifically targeted by Twitter's management, de facto as established by the linked article using an address from Tor's network put you directly under the suspicious users category.
As per the SMS check, in some country there are low-cost cellphone available as stopgap solution and requiring no identity verification during the first few weeks of usage. You may buy one, validate Twitter SMS, then dispose of it. However be concious that after such procedure your account will be linked with a phone number you do not own anymore and which will be allocated to an unknown person.
Otherwise, you may want to tackle this IP address at the root. Some VPN provider offer the possibility to get you a static dedicated IP address. Thanks to such service, you will be granted a dedicated IP address used only by you (and not shared with some other spammers), exactly like any common Internet users, but with the major difference that this IP address will be not linked to your actual location and identity. If anonymity truly matters, you will still prefer to use Tor between you and this VPN server (to ensure that no one can trace you back from the VPN provider system) and ensure that no other data can link you to this VPN server (payment system used, use Tor to subscribe a specific email account, etc.).