The ability to sense neural activity using electrodes has allowed scientists to use this information to temporarily restore movement in paralyzed individuals using brain-computer interfaces (BCI). However, current electrodes do not provide chronic recording of the brain due to the inflammatory response of the immune system caused by the large (~ 20 - 80 µm) size of the shanks, and the mechanical mismatch of the shanks relative to the brain. Electrode designs are evolving to use small (< 15 µm) flexible neural probes to minimize inflammatory responses and enable chronic use. However, their flexibility limits the scalability – it is challenging to assemble 3D arrays of such electrodes, to insert the arrays of flexible neural probes into the brain without buckling, and to uniformly distribute them into large areas of the brain. Thus, we created Shape Memory Alloy (SMA) actuated Woven Neural Probes (WNPs). A linear array of 32 flexible insulated microwires were interwoven with SMA wires resulting in an ordered array of parallel electrodes. SMA WNPs were shaped to an initial constricted profile for reliable insertion into a tissue phantom. Following insertion, the SMA wires were used as actuators to unravel the constricted WNP to distribute electrodes across large volumes. We demonstrated that the WNPs could be inserted into the brain without buckling and record neural activity. In separate experiments, we showed that the SMA could mechanically distribute the WNPs via thermally induced actuation. This work thus highlights the potential of actuatable WNPs to be used as a platform for neural recording.