Despite the current surge of interest in autonomous robotic systems, robot activity recognition within restricted indoor environments remains a formidable challenge. Conventional methods for detecting and recognizing robotic arms' activities often rely on vision-based or light detection and ranging (LiDAR) sensors, which require line-of-sight (LoS) access and may raise privacy concerns, for example, in nursing facilities. This research pioneers an innovative approach harnessing channel state information (CSI) measured from WiFi signals, subtly influenced by the activity of robotic arms. We developed an attention-based network to classify eight distinct activities performed by a Franka Emika robotic arm in different situations. Our proposed bidirectional vision transformer-concatenated (BiVTC) methodology aspires to predict robotic arm activities accurately, even when trained on activities with different velocities, all without dependency on external or internal sensors or visual aids. Considering the high dependency of CSI data on the environment motivated us to study the problem of sniffer location selection, by systematically changing the sniffer's location and collecting different sets of data. Finally, this paper also marks the first publication of the CSI data of eight distinct robotic arm activities, collectively referred to as RoboFiSense. This initiative aims to provide a benchmark dataset and baselines to the research community, fostering advancements in the field of robotics sensing.