Parameter variations introduced by manufacturing imprecision are becoming more influential on circuit performance. This is especially the case in emerging Nanoscale Cognitive Computing Fabrics due to unconventional manufacturing steps and aggressive scaling. On-chip variation sensors are gaining in importance since post-fabrication compensation techniques can be employed. In estimation with on-chip variation sensors, however, random variations are masked because of well-known averaging effects during measurements. We propose a new on-chip sensor for Nanoscale Cognitive Computing Fabrics to estimate random variations in physical parameters. We show detailed estimation methodology and validate it with Monte Carlo simulations. The results show the sensor estimation error to be 8% on average and 12.7% in worst case. In comparison to the well-known ring-oscillator based approach developed for CMOS, the estimation accuracy is 1.6X better and requires 40X less devices in on-chip sensors.