We present the results of a semicoherent search for continuous gravitational waves from the low-mass X-ray binary Scorpius X-1 , using data from the first Advanced LIGO observing run . The search method uses details of the modelled , parametrized continuous signal to combine coherently data separated by less than a specified coherence time , which can be adjusted to trade off sensitivity against computational cost . A search was conducted over the frequency range from 25 \text { Hz } to 2000 \text { Hz } , spanning the current observationally-constrained range of the binary orbital parameters . No significant detection candidates were found , and frequency-dependent upper limits were set using a combination of sensitivity estimates and simulated signal injections . The most stringent upper limit was set at 175 \text { Hz } , with comparable limits set across the most sensitive frequency range from 100 \text { Hz } to 200 \text { Hz } . At this frequency , the 95 % upper limit on signal amplitude h _ { 0 } is 2.3 \times 10 ^ { -25 } marginalized over the unknown inclination angle of the neutron star ’ s spin , and 8.0 \times 10 ^ { -26 } assuming the best orientation ( which results in circularly polarized gravitational waves ) . These limits are a factor of 3-4 stronger than those set by other analyses of the same data , and a factor of \sim 7 stronger than the best upper limits set using initial LIGO data . In the vicinity of 100 \text { Hz } , the limits are a factor of between 1.2 and 3.5 above the predictions of the torque balance model , depending on inclination angle ; if the most likely inclination angle of 44 ^ { \circ } is assumed , they are within a factor of 1.7 .