Using a phone during الطواف is جائز when the phone is being used as a tool to aid the worship — such as reading القرآن from a القرآن application, accessing a دعاء collection, or using a counter app to track the circuits of الطواف. These are modern tools that serve the same purpose as a printed دعاء book, which scholars have always permitted during الطواف. Reading from a book during الطواف was practiced by some of the Salaf.
الشيخ ابن عثيمين, while he did not address smartphones specifically, stated that reading الأدعية from a book during الطواف is جائز. By extension, contemporary scholars permit using a phone application for the same purpose. The key is that the phone is being used for worship-related purposes, not for worldly distractions.
However, scholars unanimously discourage non-worship phone use during الطواف: taking or making phone calls, sending messages, browsing social media, or taking selfies. These activities distract the الحاج from the remembrance of Allah, which is the primary purpose of الطواف. The اللجنة الدائمة has advised الحجاج to minimize distractions during the rites and to focus their hearts and minds on worship. If a phone call is genuinely urgent, the الحاج may step aside, as breaks during الطواف are جائز, take the call, and then resume their الطواف from where they stopped.