If I take online college courses and work a job, can I be classified as a full time student?

Neither working full time or taking only online courses prevents you being classified as a full time student.

Why do you ask; that is what tax benefit are you seeking or what tax negative are you trying to avoid? 

References:

https://www.investopedia.com/terms/f/fulltimestudent.asp#:~:text=According%20to%20the%20IRS%2C%20full,five%20months%20per%20calendar%20year.

https://www.usnews.com/education/online-education/articles/2016-01-29/decide-between-part-time-full-time-online-degree-programs#:~:text=Depending%20on%20an%20online%20program's,at%20the%20institution%2C%20experts%20say.

It depends.  Typically, whether you are a full-time or part-time student depends on the number of credit hours you are taking each semester.   According to the IRS, full-time students are children under the age of 19 or adults under the age of 24 who attend an educational program at least five months per calendar year.  Undergraduates are considered full-time college students if they take at least 12 credits — about four classes — each semester.

 You should check with the college you are attending to see what their requirement is to be considered a full-time student.