High-resolution transmission spectroscopy is a method for understanding the chemical and physical properties of upper exoplanetary atmospheres. Due to large absorption cross-sections, resonance lines of atomic sodium D-lines (at 5889.95 and 5895.92 angstrom) produce large transmission signals. Our aim is to unveil the physical properties of WASP-17b through an accurate measurement of the sodium absorption in the transmission spectrum. We analyze 37 high-resolution spectra observed during a single transit of WASP-17b with the MIKE instrument on the 6.5 m Magellan Telescopes. We exclude stellar flaring activity during the observations by analyzing the temporal variations of H-alpha and Ca II infrared triplet (IRT) lines. We then obtain the excess absorption light curves in wavelength bands of 0.75, 1, 1.5, and 3 angstrom around the center of each sodium line (i.e., the light curve approach). We model the effects of differential limb-darkening, and the changing planetary radial velocity on the light curves. We also analyze the sodium absorption directly in the transmission spectrum, which is obtained by dividing in-transit by out-of-transit spectra (i.e., the division approach). We then compare our measurements with a radiative transfer atmospheric model. Our analysis results in a tentative detection of exoplanetary sodium: we measure the width and amplitude of the exoplanetary sodium feature to be sigma(Na) = (0.128 +/- 0.078) angstrom and A(Na) = (1.7 +/- 0.9)\% in the excess light curve approach and sigma(Na) = (0.850 +/- 0.034) angstrom and A(Na) = (1.3 +/- 0.6)\% in the division approach. By comparing our measurements with a simple atmospheric model, we retrieve an atmospheric temperature of 1550-(200) K+170 and radius (at 0.1 bar) of 1.81 +/- 0.02 R-Jup for WASP-17b.