Was raksha bandhan practised in Ramayana period?

 rakṣā (रक्षा) : A sort of bracelet, a twist of thread or tinsel, with a small packet containing a few carminative seeds, bound round the wrist at particular periods, viz, puja, yagna, marriages, etc, to protect from any evils.

The ritual thread is traditionally worn on the right wrist or arm by the males and on the left by the females.

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Now a days, Raksha Bandhan has become an annual celebration day, with a limited meaning, when sisters of all ages tie a talisman or amulet called the rakhi around the wrists of their brothers. They symbolically protect them, receive a gift in return, and traditionally invest the brothers with a share of the responsibility of their potential care.

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Starting from the suktas or hymns of Rig Veda to many puranas, it is common practice to invoke the DIVINE GRACE of the Almighty for protection.

However, a parallel practice of tying a rakṣā (रक्षा) by a mother to children, a wife to a husband, etc, invoking the grace of NATURAL FORCES/GOD for protection, can be observed in Puranas or Ithihasa.

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1) Chapter 137 of the Uttara Parva of the Bhavishya Purana narrates the story of Sachi, the wife of Indra, tying a rakṣā (रक्षा) around the wrist of her husband, on the day of Shravana Purnima, due to which he won the battle against the demons.

2) In Ramayana, when Shri Rama declares his decision before his mother Kausalya, to proceed to the Forest in order to honour the word given by his father King Dasaratha, she invokes the blessings of various gods for protecting Shri Rama against all types of evils and ties a rakṣā (रक्षा).

इति पुत्रस्य शेषाश्च कृत्वा शिरसि भामिनी || २-२५-३७
गन्दांश्चापि समालभ्य राममायतलो चना |
ओषधीम् च अपि सिद्ध अर्थाम् विशल्य करणीम् शुभाम् || २-२५-३८
चकार रक्षाम् कौसल्या मन्त्रैः अभिजजाप च |

Saying so, Kausalya, the large eyed proud woman placed some unbroken rice grains on her son's head, smeared varieties of sandal pastes over his body, fastened about his wrist by way of an amulet - a rakṣā (रक्षा), a herb called Visalyakarani (so called because it helps in painlessly extracting an arrow stuck into one's body ), which is efficacious and auspicious and muttered sacred hymns in order to enhance its virtue.