We present adaptive optics assisted integral field spectroscopy of 34 star–forming galaxies at z = 0.8–3.3 selected from the HiZELS narrow-band survey . We measure the kinematics of the ionised interstellar medium on \sim 1 kpc scales , and show that the galaxies are turbulent , with a median ratio of rotational to dispersion support of V / \sigma = 0.82 \pm 0.13 . We combine the dynamics with high-resolution rest-frame optical imaging and extract emission line rotation curves . We show that high–redshift star–forming galaxies follow a similar power-law trend in specific angular momentum with stellar mass as that of local late type galaxies . We exploit the high resolution of our data and examine the radial distribution of angular momentum within each galaxy by constructing total angular momentum profiles . Although the stellar mass of a typical star–forming galaxy is expected to grow by a factor \sim 8 in the \sim 5 Gyrs between z \sim 3.3 and z \sim 0.8 , we show that the internal distribution of angular momentum becomes less centrally concentrated in this period i.e the angular momentum grows outwards . To interpret our observations , we exploit the EAGLE simulation and trace the angular momentum evolution of star–forming galaxies from z \sim 3 to z \sim 0 , identifying a similar trend of decreasing angular momentum concentration . This change is attributed to a combination of gas accretion in the outer disk , and feedback that preferentially arises from the central regions of the galaxy . We discuss how the combination of the growing bulge and angular momentum stabilises the disk and gives rise to the Hubble sequence .