"To assign a score" means to give or allocate a numerical value or rating to something based on certain criteria. It is a way of quantifying or evaluating the quality, performance, or importance of that thing. Full definition
Using questionnaires and interviews, each participant was assigned a score based on the severity of the abuse or neglect experienced during childhood. (sciencedaily.com)
We're going to use science and mathematics here, assigning scores from 1 - 10 in each of the three categories. (sbnation.com)
And by assigning a score to your happiness, you can begin to see what matters to your day and what doesn't. (canadianbusiness.com)