When the work must conform to AWS D1.1, which is the structural welding code for steel, the required qualifications, which include persons who can certify a welder, are found in 6.1.4 Inspector Qualification Requirements. Just remember that the project specifications can override 6.1.4.
I have no formal schooling or special training that allows me to certify welders, but the verbiage in 6.1.4 allows me to do so based on my experience. Again, the job specs can override what D1.1 allows.