The outage began around 3 p.m. BST and appeared to last about 30 minutes.
The DownDetector website monitor has logged thousands of reports of users having difficulty signing in.
The highest concentration of reports came from Japan, according to a map of the outages.
Users in the UK, the Netherlands, and the US have also reported issues with the service.
The independent contacted Twitter for details.
Twitter support wrote in a successful tweet after the outage: “Let’s see if this works… You may have had trouble sending and seeing Tweets. (Yeah, so do we.) We’ve now fixed that problem. ”