According to a report by The Financial Times, which also links to discussions on Apple's Support Communities, hundreds of customers have complained about the issue.
Rebooting and other troubleshooting steps don't seem to resolve the issue, and it is unclear how many people are affected by the issue.
Frustrated users also took to Twitter and Reddit to report the issue.
Twitter user Mahesh Juvekar wrote: "@Apple when are you gong to sort iPhone X call display issue???"
Twitter user Vishal Shah complained that iPhone service centers in India failed to fix iPhone X's with this problem, while in the US phones with the glitch are replaced quickly.
Reddit user barryc56 wrote: "Some friends are having delay issues, call rings like 2 times in apple watch before the Iphone X start ringing and screen goes on, any solution?"
The problem hasn't been resolved in the latest iOS 11.2.5 software update, and based on user accounts it seems that the problem can be traced back to all versions from iOS 11.2 onwards.
Earlier versions of iOS 11, however, could be affected too.
According to MacRumors, Apple is likely collecting data from customers experiencing the problem so that its engineers can look into it - as it does with any potential software or hardware issues.
Affected users should contact Apple Support, as the problem is likely to be addressed in an upcoming software update.
This isn't the only problem that has faced iPhone X users.
In November 2017, some iPhone X users reported that their screens became unresponsive in the cold weather, in a glitch dubbed "coldgate".
Also in November 2017, some iPhone X users reported a glitch that caused a green line to appear on the phone's screen.
According to recent reports, the iPhone X's disappointing sales could lead to the phone being cancelled - with production stopping as soon as this summer.