We describe a genetically encoded micelle for targeted delivery consisting of a diblock polypeptide with segments derived from repetitive protein motifs inspired by Drosophila melanogaster Rec-1 resilin and human tropoelastin with a C-terminal fusion of an integrin-targeting fibronectin type III domain. By systematically varying the weight fraction of the hydrophilic elastin-like polypeptide (ELP) block and molecular weight of the diblock polypeptide, we designed micelles of different morphologies that modulate the binding avidity of the human wild-type 10th fibronectin domain (Fn3) as a function of shape. We show that wormlike micelles that present the Fn3 domain have a 1000-fold greater avidity for the α_v β₃ receptor compared to the monomer ligand and an avidity that is greater than a clinically relevant antibody that is driven by their multivalency. The amplified avidity of these micelles leads to significantly increased cellular internalization, a feature that may have utility for the intracellular delivery of drugs that are loaded into the core of these micelles.