The rotationally resolved spectrum of the B$^2Pi-$X$^2Pi$ electronic origin band transition of $^{13}$C$_6$H is presented. The spectrum is recorded using cavity ring-down spectroscopy in combination with supersonic plasma jets by discharging a $^{13}$C$_2$H$_2$/He/Ar gas mixture. A detailed analysis of more than a hundred fully-resolved transitions allows for an accurate determination of the spectroscopic parameters for both the ground and electronically excited state of $^{13}$C$_6$H.