Actually, Turks accepted Islam by themselves. I explained this question very detailed, so be ready?

In Umayyad times, Turks didn't think that Islam was a good religion because the Umayyad Caliphate treated no-Arab citizens like slaves and the Caliphate was fighting Turkish Khanagates to control Central Asia. Arabs were invading Central Asia and defeating the Turks but the process was slow.

After the fall of Umayyad Caliphate, the Abbasid Caliphate got control over the empire. In 751, Abbasids were controlling east of Central Asia and China was controlling almost all of Central Asia. Turks almost didn't have any landmass left. Turks didn't want to China to control Central Asia because Central Asian Turkic Khanagates hated China. So they agreed to fight with the Abbasid Caliphate in the Battle of Talas. Abbasids won the battle.

Abbasids thought that Islam was a free religion. So they introduced Turks with Islam. Turks liked Islam because it was very similar to their previous religion, "Tengri" or "Gök Tanrı". Turks recognized Islam as their own religion and started to spread their religion everywhere. It was easier for them because they were nomads.

But not all Turks became Muslim. Only most of Turks became Muslim. Volga Bulgarians stayed Christian, Khazars stayed Jewish, Uygurs believed in Manichaeism and some Turkic tribes still believed in Tengri. However sometime later Islam spread more in Turks but even now there are lots of Turks who don't believe in Islam.