All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
We ask Allah to increase you in aspiring toward good and to reward you for your keenness to avoid prohibitions. Regarding replacing the music as a ringtone on your telephone with the azan, it is a good deed that involves no blame, Allah willing. However, care should be taken to keep the volume low in order not to confuse people as they might think that the time for prayer has begun. Some Shaafi‘i jurisprudents stated some situations in which the azan is proclaimed for reasons other than the prayer. In Tuhfat Al-Muhtaj, it is said, The azan is enacted for other than prayer, as in the azan for the newborn, the distressed, the epileptic, the angered, the ill-mannered, and so on.
Allah knows best.