Terminal deoxynucleotidyl transferase (TdT) enzyme plays an integral part in the V(D)J recombination, allowing for the huge diversity in expression of immunoglobulins and T-cell receptors within lymphocytes, through their unique ability to incorporate single nucleotides into oligonucleotides without the need of a template. The role played by TdT in lymphocytes precursors found in early vertebrates is not known. In this paper, we demonstrated a new screening method that utilises TdT to form libraries of variable sized (vsDNA) libraries of polynucleotides that displayed binding towards protein targets. The extent of binding and size distribution of each vsDNA library towards their respective protein target can be controlled through the alteration of different reaction conditions such as time of reaction, nucleotide ratio and initiator concentration raising the possibility for the rational design of aptamers prior to screening. The new approach, allows for the screening of aptamers based on size as well as sequence in a single round, which minimises PCR bias. We converted the protein bound sequences to dsDNA using rapid amplification of variable ends assays (RAVE) and sequenced them using next generation sequencing. The resultant aptamers demonstrated low nanomolar binding and high selectivity towards their respective targets.