You can do a software marketing career and excel on it even without a solid computer science background. However, somehow you will be expected to have some It knowledge. I may say that IT Marketing could be a nice course for you or any other equivalent or related courses. Some of these courses could be Outsourcing and IT Based Business, Technology Strategy Consulting and a lot more. You can be an effective marketing person if you have a good grasp of the IT industry. You can offer much better digital marketing solutions if you know the ins and out of the software or IT industry.