While you might choose for your character to be born into a country where their parents might arrange for you to be married to someone, you do have the option to reject the match your in-game parents present you with.
Rejecting this arranged marriage, though, might not always be the best option for your character, depending on your end goal. Rejecting an arranged marriage will decrease your relationship with your parents in the game, and multiple rejections will only further hurt it.
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No matter why you reject the first person your parents arrange for you to marry in the game, it's possible your parents will continue to propose you marry the same person. You have the option this time whether or not to marry their chosen partner, though continuous rejection will not help your relationship with your parents.
If you choose to marry the person your parents to you, you always have the option to divorce them later down the line.
If your character is seeing someone else at the time that your parents propose an arranged marriage, you also have the option to interrupt the marriage ceremony and wed another character. This, of course, would also hurt your relationship with your parents, so it's best to weigh your options before making the decision.