Reference: al-Muntaqaa min Fataawa Shaykh Saalih al-Fowzaan – Volume 2, Page 35, Fatwa No.15
Question: Is it obligatory to face the Qiblah (direction of the Ka’bah in Makkah) whilst reciting [the Qur.aan]?
Response: It is befitting to face the Qiblah [whilst doing so], since reciting the Qur.aan is [an act of] worship, and it is recommended for [an act of] worship to be done whilst facing the Qiblah. So if this is easily possible then it is [regarded as] from the completeness [of the act of worship]. [However], if one does not face the Qiblah, then there is no harm in that.