We propose a spectrally agile far-infrared detector based on an InSb n-i-p-i superlattice. We show that the spectral response of the detector can be tuned with an applied electrical bias that modulates the tunneling-assisted interband absorption coefficient by changing the internal electric fields. Calculations for several possible superlattice designs are presented and the limitation on the design parameters imposed by the tunneling current is discussed. It is shown that the detector can distinguish between blackbodies with temperatures in the range of 200-400 K independent of the distance between the object and the detector. We also present a simple discussion of the response time that can be expected from such a detector and of the noise sources that will limit its performance.