The call to prayer or Azan is an age old Islamic tradition known to Muslims in every society. It's sound is hypnotic and fills the air with the sound of God's name. In Hadithist (Sunni) and Shi'a traditions the Azan includes the names of the Prophet Muhammad and Ali respectively.
As Quranism is concerned with God alone worship based on the Qur'an but including traditions from Islamic cultures (where they are in harmony with Qur'anic rulings) the Azan can be used as a beautifier to Quranist spirituality.
The Qur'an states:
You shall commemorate the name of your Sustainer, to come ever closer and closer to Him. [73:8]
Thus if the Azan is used to:
a) commemorate the name of God
b) bring peoplee closer to God (especially for the purpose of prayer)
then it is not something that is forbidden but encouraged.
Personally I like the version of Quranist Azan that recited Allahu Akbar x4 followed by La ilaha ila Allah x1 because being lengthier it allows for variation in style and sounds closer to the Hadithist/Shia versions which are well known worldwide.
Here is a version in Persian style recited by a woman:
