Is converting a categorical value into numerical needed to find a correlation?
Your categorical feature is an ordinal one meaning it conveys an order between the levels that represent it. So you can convert it to a numerical feature, however the difference between 2 consecutive levels is unknown and cannot be translated into numbers.

Example : High - Medium - Low --> 3 - 2 - 1 or 4 - 2 - 1 or 5 - 2 - 1. 
See? The order is preserved but the difference between the levels is arbitrary.

Also you oughta now that picking values for your feature affect correlation due to the fact that you're free to pick any values you want for your categorical feature.