Should I wait for ICU job because I will become a CRNA in the future, or take a nursing job in another department in the meantime?

You'll need a nursing degree; BSN or higher, your RN licensure, and 2-3.5 years of ICU experience before being accepted into a CRNA program. You might be able to get into an ICU as a new grad, but traditionally, it is beneficial to have a year of general medical/surgical unit experience. I would advise getting any experience while waiting for an ICU position. Best of luck!

Get into critical care and focus on your goal. Other departments are not in your endgoal unless you just want to add on to your resume.
I would go straight to critical care… ICU/Trauma/ER

ICU - many schools require that experience,

Experience is key here ER usually is terrific for the experience or even CCU