Using a phone during Tawaf is boleh when the phone is being used as a tool to aid the worship — such as reading Al-Quran from a Al-Quran application, accessing a doa collection, or using a counter app to track the circuits of Tawaf. These are modern tools that serve the same purpose as a printed doa book, which scholars have always permitted during Tawaf. Reading from a book during Tawaf was practiced by some of the Salaf.
Sheikh Ibn Uthaymeen, while he did not address smartphones specifically, stated that reading doa-doa from a book during Tawaf is boleh. 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 Tawaf: taking or making phone calls, sending messages, browsing social media, or taking selfies. These activities distract the jamaah haji from the remembrance of Allah, which is the primary purpose of Tawaf. The Permanent Committee has advised jamaah haji to minimize distractions during the rites and to focus their hearts and minds on worship. If a phone call is genuinely urgent, the jamaah haji may step aside, as breaks during Tawaf are boleh, take the call, and then resume their Tawaf from where they stopped.