Technically "has" is correct for a countable noun like "quarter" because "a quarter", singular, is the subject of the sentence. However there is also a concept of "overriding" in English grammar and in this case the complement of the subject (respondents) is plural and I would say overrides the singular subject. Most English speakers in my opinion would say, "A quarter of the respondents have been working ..." and since grammar describes usage I'd say either is acceptable. However you would have to say, "A quarter of the respondents consists (NOT consist) of people who work in the IT industry" because in this case the emphasis is entirely on the proportion (a quarter), rather than the people and where they work.

quarter is singular, so has; if you wrote three quarters that is obviously plural, have

3rd person plural, if I am not mistaking- "Have."

I think most native English speakers would use "have" here and the same would be true for the following sentence, which clearly involves only one person. One quarter of the four people who responded have worked in the IT industry.

‘quarter’ can be plural or singular. ‘A quarter of the respondents’ (= many respondents (plural)) He’ll inherit a quarter of the company someday. A quarter of the company is worth a lot. (= ONE quarter (singular))