We present constraints on a cosmic string network with a measurement of weak gravitational lensing from CMB temperature map. The cosmic string network between the observer and last scattering surface of CMB photons generates vector and/or tensor metric perturbations, and the deflection of CMB photons by these gravitational fields has a curl mode which is not produced by the scalar metric perturbations. In this paper, we use the power spectrum of curl mode obtained from Planck to constrain the string tension, ??, and the reconnection probability, ?. In demonstrating the parameter constraints with Planck curl mode, we also measure the lensing power spectrum from the Atacama Cosmology Telescope (ACT) 2008 season data, which have better angular resolution with lower instrumental noise on a much smaller chunk of the sky. Assuming ? =1, the upper bound on tension is ?? =6.6 ×10−5 with 2? (95% C.L.), using curl mode from Planck, which is weaker than that from the small-scale temperature power spectrum. For small values of ?, however, the constraint from curl mode becomes tighter compared to that from the temperature power spectrum. For ? ≲10−2, we obtain the constraint on the combination of the string parameters as ???−1 ≤3.4 ×10−5 at more than 2? (95% C.L.).
