A precision measurement of the delivered luminosity is a key component of the ATLAS physics program at the Large Hadron Collider (LHC). A fundamental ingredient of the strategy to control the systematic uncertainties affecting the absolute luminosity has been to compare the measurements of several luminometers, most of which use more than one counting technique. The level of consistency across the various methods provides valuable cross-checks as well as an estimate of the detector-related systematic uncertainties. This poster describes the development of a luminosity algorithm based on pixel-cluster counting in the recently installed ATLAS inner b-layer (IBL), using data recorded during the 2015 pp run at the LHC. The noise and background contamination of the luminosity-associated cluster count is minimized by a multi-component fit to the measured cluster-size distribution in the forward pixel modules of the IBL. The linearity, long-term stability and statistical precision of the cluster-counting method are characterized by comparison with several other ATLAS luminometers.