The right direction is synonymous with the right actions. So, the right hand is considered auspicious to tie Rakhi on the wrist of the brothers as it is believed that it will show him the right path.
Another aspect of using the right hand for religious ceremonies like tying a Rakhi is based on Ayurveda Science. This ancient system stresses the use of the right hand for Rakhi tying as it regulates Vata, Pitta, and Kapha doshas. When a rakhi is tied on the right hand of the brother by a sister, these elements of the human body get regulated resulting in well-being.
In Nadi Shastra, the human body has three Nadis – Ida, Pingala, and Sushumna. Pingala Nadi is on the right side of the body linked to masculinity and imparts efficiency, strength, and vitality.