The Fairbairn One Name Study has an accompanying Surname DNA project at FamilyTreeDNA.

The DNA project welcomes anyone with a genetic connection to the Fairbairn, or variant, surnames.

Although this One Name Study is for the Fairbairn surname (as there’s a separate ONS for the – more English – Fairburn surname,) the DNA project is all inclusive and welcomes all variants.

Public analysis of the results is skewed towards the direct male line Fairbairn variants, along with those who match them.
However with the advent of autosomal DNA testing (FamilyTree DNA’s FamilyFinder test, or the tests offered by Ancestry, MyHeritage and 23andme) DNA testing need not remain the preserve of the Fairbairn males, so anyone with a Fairbairn ancestor within the reach of autosomal DNA is welcome and there is a growing collection of data from autosomal results.

Statistics for those in the Fairbairn and variants Surname project at FamilyTreeDNA can be viewed at  this project page.
As at Sep 2017 the project contained 88 members, 63 of whom were yDNA tested males at various levels of precision, ranging from 1 only tested at 12 markers through to 8 with the current ultimate test – BigY.
50 have tested at the recommended yDNA67, 8 of whom have been upgraded to the more precise 111 markers.

Analysis outwith the formal Fairbairn DNA project at FamilyTreeDNA however includes data from other sources, notably autosomal DNA results from any company, and shared at the cross-company site

On this site, keep an eye on the Trees Pages, eg
search the Histories pages for DNA