We present results from an analysis looking for dark matter annihilation in the Sun with the IceCube neutrino telescope. Gravitationally trapped dark matter in the Sun's core can annihilate into Standard Model particles making the Sun a source of GeV neutrinos. IceCube is able to detect neutrinos with energies >100 GeV while its low-energy infill array DeepCore extends this to >10 GeV. This analysis uses data gathered in the austral winters between May 2011 and May 2014, corresponding to 532 days of livetime when the Sun, being below the horizon, is a source of up-going neutrino events, easiest to discriminate against the dominant background of atmospheric muons. The sensitivity is a factor of two to four better than previous searches due to additional statistics and improved analysis methods involving better background rejection and reconstructions. The resultant upper limits on the spin-dependent dark matter-proton scattering cross section reach down to 1.46×10-5 pb for a dark matter particle of mass 500 GeV annihilating exclusively into τ+τ- particles. These are currently the most stringent limits on the spin-dependent dark matter-proton scattering cross section for WIMP masses above 50 GeV.