If you will be acting in a play or a musical, you will have to memorize the script, although you won’t be expected to remember all the lines immediately. The first few rehearsals, you can still hold your script. But it’s best, to memorize your lines as soon as possible. You can focus on your acting much more once you know your lines.
You’re expected to practice your script at home. It’s best to practice a bit every day. That way, you’ll get more and more familiar with it; only studying your lines once or twice a week will take much more effort… How long it will take to memorize it all, that comes down to the size of your role and your memorizing talents.