The rheological properties of macromolecular and colloidal suspensions are dependent on the thermodynamic and kinetic parameters that define viscous flow, and remain an active field of study with broad implications in cellular biophysics, soft-matter theory, and biopharmaceutical technology. Here we use static light scattering, small-angle X-ray scattering, and viscosity measurements as a function of protein concentration to semiquantitatively correlate the oligomeric state of an IgG1 antibody (mAb1) with its theological behavior at solution pH 6.0 and varying ionic strength (modified by 0.01-0.1 M Na2SO4). Solution SAXS characterization of 100 mM Na2SO4 solutions confirmed that mAb1 forms reversible dimers with extended structures in dilute solutions. Light-scattering measurements over a wide range of concentrations (1-175 mg/mL) provide detailed information on the equilibrium thermodynamic mAb1 interactions and their modulation by modest increases of Na2SO4. Through the use of interacting hard sphere models to fit light-scattering data, we establish that protein cluster formations consisting of 2-9 mAb1 molecules also increase the viscosity of 175 mg/mL IgG solutions from 52 up to 450 cP. The analysis of dilute and semidilute mAb1 solution rheology correlates linearly with the thermodynamic equilibrium cluster size, consistent with the viscosity behavior of elongated oligomeric structures that are not significantly dendrimeric or in a state of globular collapse. Furthermore, SAXS- and rheology-based structural modeling illustrate that only a small set of anisotropic interactions between complementary surfaces are required to nucleate and propagate protein clusters.