To Register
登録 is registration. Make that into a verb and you have to register.
とうろくする
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.
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?