Intrinsic alignments (IA), the coherent alignment of intrinsic galaxy orientations, can be a source of a systematic error of weak lensing surveys. The redshift evolution of IA also contains information about the physics of galaxy formation and evolution. This paper presents the first measurement of IA at high redshift, $zsim 1.4$, using the spectroscopic catalog of blue star-forming galaxies of the FastSound redshift survey, with the galaxy shape information from the Canada-Hawaii-France telescope lensing survey. The IA signal is consistent with zero with power-law amplitudes fitted to the projected correlation functions for density-shape and shape-shape correlation components, $A_{delta+}=-0.0071pm 0.1340$ and $A_{++}=-0.0505pm 0.0848$, respectively. These results are consistent with those obtained from blue galaxies at lower redshifts (e.g., $A_{delta+}=0.0035_{-0.0389}^{+0.0387}$ and $A_{++}=0.0045_{-0.0168}^{+0.0166}$ at $z=0.51$ from the WiggleZ survey). The upper limit of the constrained IA amplitude corresponds to a few percent contamination to the weak-lensing shear power spectrum, resulting in systematic uncertainties on the cosmological parameter estimations by $-0.052<Delta sigma_8<0.039$ and $-0.039<Delta Omega_m<0.030$.