I am an Undergraduate Student who landed a job as a Data Scientist. Should I pursue a PhD and can I do it while working full time?
There cannot be a definite answer to your question, because we lack basic information regarding the project, arrangement etc. 

I think the best way to find out if something like that is possible is to consult your local department where you finished your BSc, the people with expertise as close as possible to your future project, who will be able to judge if this makes a valid and potentially fruitful research plan. If yes, then I do not think you will have big problems admitted to the PhD program. 

As a side note, observe that you might be asked to deal with some Master level courses/exams etc which, if you work full time, and depending how difficult is your department, will not be a piece of cake.