In regions with strongly varying electron density , radio emission can be magnified significantly by plasma lensing . In the presence of magnetic fields , magnification in time and frequency will be different for two circular polarizations . We show how these effects can be used to measure or constrain the magnetic field parallel to the line of sight , B _ { \parallel } , as well as its spatial structure , \sigma _ { B _ { \parallel } } , in the lensing region . In addition , we discuss how generalized Faraday rotation can constrain the strength of the perpendicular field , B _ { \perp } . We attempt to make such measurements for the Black Widow pulsar , PSR B1957+20 , in which plasma lensing was recently discovered . For this system , pressure equilibrium suggests B \gtrsim 20 G at the interface between the pulsar and companion winds , where the radio eclipse starts and ends , and where most lensing occurs . We find no evidence for large-scale magnetic fields , with , on average , B _ { \parallel } = 0.02 \pm 0.09 G over the egress lensing region . From individual lensing events , we strongly constrain small scale magnetic structure to \sigma _ { B } < 10 mG , thus excluding scenarios with a strong but rapidly varying field . Finally , from the lack of reduction of average circular polarization in the same region , we rule out a strong , quasi-transverse field . We can not identify any plausible scenario in which a large magnetic field in this system is concealed , leaving the nature of the interface between the pulsar and companion winds an enigma . Our method can be applied to other sources showing plasma lensing , including other eclipsing pulsars and fast radio bursts , to study the local properties of the magnetic field .