Consulting during PhD?
Is the question really as you are asking if this is possible? Well, more improbable things are possible, so clearly yes. The specifics of your situation, and the type of consulting are both important. Are you already in a PhD and have a concrete oportunity? (asking the question conditional on PhD and opportunity) Are you already in a PhD and consider looking for opportunities but do not have something concrete? (asking the question conditional on PhD only) Are you considering a PhD and want to see what your prospects for a stipend on the side would be? Do you have the opportunity but consider the PhD? Why do you want to get the PhD / what do you think you ll do after (your profile is not suggesting you want to continue in academia after the PhD, am I wrong?)

In any case, keep in mind that the most important factors are:

-If you are already in a PhD and have one: your advisor. What does he think? Can he help you find something relevant to your thesis/ help you get exerience / connections? Talk to him and make sure he is ok. He might also be able to provide good alternatives

-A think you learn with experience: A PhD should not be a lengthy affair. Every year counts and you want to finish as soon as possible. Especially in a field like yours (ours ;)) you can have a lot of opportunities to get paid for doing the PhD... Do you really need the extra stipend if it will delay you? Unless you get something other than money back, that you can use for your thesis or after the phd.

-What you want to do after the PhD. The PhD is a lousy end goal, it can only serve as the means to an end. What is your optimization function? What do you want to get out of your PhD? How is the extra activity going to help you?

-If you have not yet started the PhD yet, and you really care about that stipend, it might be worth noting that there are many situations where the converse might be more productive and easier, especially given your profile: getting a PhD while working in industry, You would have to find a company (more difficult part, they pay...) and an advisor (easier part: they do not have to support financially, and they get money and a PhD student) willing to support you while doing the phd... You (and secondary the advisor) will want to make sure that the company commits in paper for at least a number of years though(i would suggest minimum 3): otherwise its possible a year in the future the company's scope will change /money will run out