Biological age is typically estimated using biomarkers whose states have been observed to correlate with chronological age. A persistent limitation of such aging clocks is that it is difficult to establish how the biomarker states are related to the mechanisms of aging. Somatic mutations could potentially form the basis for a more fundamental aging clock since the mutations are both markers and drivers of aging and have a natural timescale. Such a timer has been impractical thus far, however, because detection of somatic variants in single cells presents a significant technological challenge. Cell lineage trees built out of these mutations are phylogenetic structures that can help quantify somatic evolution. The central conjecture behind our aging timer approach is that the shape, that is the combination of branch lengths and branching patterns, of cell lineage trees is predictive of the aging status of the body. Here we show that somatic mutations detected using single-cell RNA sequencing (scRNA-seq) from hundreds or thousands of cells can be used to construct a cell lineage tree whose shape correlates with chronological age. Single-nucleotide variants (SNVs) are detected de novo in human peripheral blood mononuclear cells using a modified protocol. Penalized multiple regression is used to select from over 30 possible metrics characterizing the shape of the phylogenetic tree resulting in a Pearson correlation of 0.8 between predicted and chronological age and a median absolute error of ~6 years. The geometry of the cell lineage tree records the structure of somatic evolution in the individual and represents a new modality for aging timers. In addition to providing an estimate for biological age, it unveils a temporal history of the aging process, revealing how clonal structure evolves over lifespan. Cell Tree Rings as a foundational component and integrative framework of combined clocks might mitigate the current uncertainty in the assessment of geroprotective trials.