We report the results of a directed search for continuous gravitational-wave emission in a broad frequency range ( between 50 and 1000 Hz ) from the central compact object of the supernova remnant Cassiopeia A ( Cas A ) . The data comes from the sixth science run of LIGO and the search is performed on the volunteer distributed computing network Einstein @ Home . We find no significant signal candidate , and set the most constraining upper limits to date on the gravitational-wave emission from Cas A , which beat the indirect age-based upper limit across the entire search range . At 170 Hz ( the most sensitive frequency range ) , we set 90 \% confidence upper limits on the gravitational wave amplitude h _ { 0 } of \sim ~ { } 2.9 \times 10 ^ { -25 } , roughly twice as constraining as the upper limits from previous searches on Cas A . The upper limits can also be expressed as constraints on the ellipticity of Cas A ; with a few reasonable assumptions , we show that at gravitational-wave frequencies greater than 300 Hz , we can exclude an ellipticity of \gtrsim ~ { } 10 ^ { -5 } .