regression with ranked values

I have a problem

I want to make a regression analyse with a few independent variables and 1 dependent variable. The data is all ranked. The highest value is number 1, ... the lowest value number 220.

I want to make a prediction of the rank for the dependent variable. But can't use lineair regression because of the fact that it's ordinal data.

How do I have to make the regression analyse?
Can I do this with ordinal logistic regression? Because there are a lot categories for each variable with most of the time online one value in it.