する verb
とうろくする
臓器提供者として登録をしたきっかけは何ですか。
What motivated you to register yourself as an organ donor?
登録 is registration. Make that into a verb and you have to register.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.