Is what the patient said: "If I leave, I will memorize the entire Qur’an," considered a vow?

What transpired from you is considered a vow, and you are obligated to fulfill it. You must now strive to memorize the Quran and take all possible means to achieve it. Create a program and a timeline for memorization. If Allah's appointed time comes before you complete the memorization, then I advise that expiation be made for your vow, similar to the expiation for an oath.