This paper investigates the optimal transmit beamforming design of simultaneous wireless information and power transfer (SWIPT) in the multiuser multiple-input-single-output (MISO) downlink with specific absorption rate (SAR) constraints. We consider the power splitting technique for SWIPT, where each receiver divides the received signal into two parts: one for information decoding and the other for energy harvesting with a practical non-linear rectification model. The problem of interest is to maximize as much as possible the received signal-to-interference-plus-noise ratio (SINR) and the energy harvested for all receivers, while satisfying the transmit power and the SAR constraints by optimizing the transmit beamforming at the transmitter and the power splitting ratios at different receivers. The optimal beamforming and power splitting solutions are obtained with the aid of semidefinite programming and bisection search. Low-complexity fixed beamforming and hybrid beamforming techniques are also studied. Furthermore, we study the effect of imperfect channel information and radiation matrices, and design robust beamforming to guarantee the worst-case performance. Simulation results demonstrate that our proposed algorithms can effectively deal with the radio exposure constraints and significantly outperform the conventional transmission scheme with power backoff.