I searched this question online. I have found two theories. Theory 1 According to first theory, "rica" is an Arabic word. It is claimed that Arabic word "rica" came from another Arabic word "rücû" which has a meaning of returning, opposite... So, when some thanks to you, you say "rica ederim". In a way, you are responding that "thank you" by another "thank you". Lastly, the person who claimed this theory is saying that when you say "rica ederim" you say "I return your thank you" or just "I thank you" :) Theory 2 According to second theory, "rica ederim" comes from religious literature. It is claimed that "rica" came from "recâ" and "recâ" is a word that describes relationship with god. So, because of this reason "rica ederim" is the most polite word to describe your attitude towards to "thank you". However, both of these theories were written in comments. Unfortunately, I did not find any blog text or an academic explanation. Maybe we should ask a person who knows Arabic, Turkish and have experience with etymology.

It doesn't have a meaning. Need an etymologyc research to find out why it's used as an answer to thanking.

Ben senin işini yaptım bana teşşekür ettin ilerde benim de işim düşer sana ona göre senden rica edebilirim :D (tabiki öyle bi anlamı yok)