The VIENNA rectifier is increasingly being considered as the active front-end converter in many applications that do not require regeneration or controllable input reactive power. In such applications, this rectifier is normally operated at unity source displacement factor, which derates its nominal voltampere (VA) rating. Moreover, in the "source voltage oriented" reference frame that is normally used for control, this rectifier has complex operating limits on the rectifier terminal voltage (imposed by the operating conditions), which needs to be computed online to avoid the line currents from going through zero-crossing distortions. Also, the source voltage has to be either measured or estimated, which further increases the cost and/or computational burden. This paper proposes a control method that eliminates the requirement of the input voltage sensors (or estimators) and makes the limits on the rectifier terminal voltage far simpler to compute. The control method is implemented in the input line current oriented reference frame, considering unity displacement factor at the rectifier input terminals, which minimizes the VA rating of the rectifier (for a given rated load power). The proposed sensorless current-oriented control approach is compared with the conventional voltage-oriented control strategy through experimental results.