Automated visual tracking of cells from video microscopy has many important biomedical applications. In this paper, we track human monocyte cells in a fluorescent microscopic video using matching and linking of bipartite graphs. Tracking of cells over a pair of frames is modeled as a maximum cardinality minimum weight matching problem for a bipartite graph with a novel cost function. The tracking results are further refined using a rank-based filtering mechanism. Linking of cell trajectories over different frames are achieved through composition of bipartite matches. The proposed solution does not require any explicit motion model, is highly scalable, and, can effectively handle the entry and exit of cells. Our tracking accuracy of (97.97 ± 0.94)% is superior than several existing methods [(95.66 ± 2.39)% [11], (94.42 ± 2.08)% [20], (81.22 ± 5.75)% [13], (78.31 ± 4.70)% [14]] and is highly comparable (98.20 ± 1.22)% to a recently published algorithm [26].