Approximately 10 hours a week is a part-time job - and actually between 1/3 and 1/2 the amount of hours typical of a part-time job, so it's a very light part-time job.
These jobs exist, with caveats:
- They usually pay much less than jobs that require more hours (even half the rate is pretty uncommon, as well as having no benefits at all)
- If they pay more than the minimum wage in your area, they tend to go to people with advanced specialist skills/experience and are often temporary (less than a year) or in short supply
- Most jobs that require so few hours have special requirements (so not just anyone is eligible, experience or not), or are labor jobs like cleaning, or require work at late/early hours (like bar-tending)
The main question is: how cheaply can you live, and thus how much money is enough for you? If you need $10 an hour, many cities will have work you could potentially do for this rate and be ok with such a short amount of time. If you are looking for a rate of closer to what is typical of a full-time entry-level programmer based on your degree, that's probably not going to happen - but hats off if you manage it somehow!
The most common jobs that will fit you are ones explicitly designed for students, on-campus jobs especially. You might consider help desk or IT at your future University, as they often have positions that require a bit more experience and thus pay a bit more. However, you may find that many of them prefer undergrads who are working on a degree in the field - and they may or may not even consider you for the positions based on your current degree focus. Won't know until you try, though.
Some might point to "consulting", but generally this takes way, way, more than 10 hours to get established with any degree of regularity and will not generally be something that you can do, be well paid, and allow you to focus on your other unrelated studies. I have no positive opinions towards online freelance groups, and don't personally know anyone who does - they seem more geared for offshore labor or low-paid "just because" tasks (like Mechanical Turk), but YMMV.
Depending on your school, you might be able to check in with the computing-related department and see if there are projects you could work on there (as there just aren't always enough undergrads who want to work and have the required skills). Such assignments and projects usually aren't official research assistants or teaching assistants, don't take a lot of hours per week, but are often not steady work (it might just be a month-long project and then you are effectively unemployed again). The pay can be good, depending on the department - sometimes double the rate of regular student employment, if the department has trouble finding undergrads or grad students who want to work on small projects. These are commonly word-of-mouth or email to department only, so if you don't talk with them you might not ever hear about them.
So all in all it's doable, but you will need to be aware that you are extremely unlikely to find a position that pays a rate similar to what 4-year CS grads make in full-time positions and that allows you to work for such a short amount of time per week.