Typically a degree in linguistics (including with a computational focus) will not teach you the technical skills you need to do computational linguistics. Most people who do that already have the background or get it on their own. There may be some programs that do teach this, but not all do. So you might need to get a degree in computer science first, or learn it on your own, and then possibly also get an MA or PhD in (computational) linguistics. It depends on exactly what you're going for. If you want a job, you probably only need the relevant computer skills. If you want to be a professor of (computational) linguistics, you'll need a PhD in linguistics.

Note that there are different kinds of jobs in "computational linguistics"-- some are for linguists who know a little about programming and can work with programmers. But most are for programmers who know a little (or a lot) about linguistics.

Some programs are moving in the direction of teaching more about computational skills, such as adding combined bachelor's programs that have both computer science and linguistics, but you may still need to pursue one or the other at a higher level to get certain jobs.