Measuring the concentration of amino acids "in the body" is a bit difficult. Your body is made up of lots of cells and organs, each one of which exists in a constant state of flux and contains many proteins and amino acids.
Assuming perhaps that you meant "in the blood", then yes, such kits do exist -- e.g. this enzyme-linked spectrophotomeric assay -- https://www.antibodies-online.com/kit/1503021/Cysteine+ELISA+Kit/ -- but it costs €642,85 (+€40 shipping and 22% VAT) for 96 tests, and requires a molecular biology laboratory to use.
The only commonly performed similar tests I am aware of are whole plasma amino acid counts, commonly performed on infants to look for inborn errors of metabolism -- i.e. specific birth defects of metabolism. You can find an example US Hospital page here that contains the reference range for each amino acid.