Both answers are grammatically correct. The words have very similar meanings. However, there is a slight difference in meanings which relate to their different original meanings.
Regard comes from regarder, meaning to look at. Native English speakers will usually use this word with something specific, something that can be looked at. So, if you saw an advertisement for a job, it would be quite acceptable to say, I'm calling regarding your ad for a job opening as a waiter. However, if you don't know if there are any job openings, then there's nothing specific to look at, so many native English speakers would be more likely to use about in that case. However, other native English speakers may use them almost interchangeably - I don't but I'll allow that others may.
About comes from onbūtan meaning on the outside of. It is therefore more appropriate if things are less specific and if one wants to refer to a subject area. So if you have no idea if there is a job available, but want to find out whether one might be available, then the word about is more natural - you are interested in the subject area of possible jobs as a waiter and are not responding to specific job advertisement.
Based on your options, it appears you are trying to find out if there are any available jobs, and therefore a little more precise is I'm calling about a job opening as a waiter."
Regarding ЯegDwight's claim in another answer that regard is higher register than about, I think that's rubbish. To wit,
"Much Ado about Nothing" - play by William Shakespeare
"You regard me as a kind of ancient crone..." - Groucho Marx
Either word works fine in any register.