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. Cell lineage trees inferred from these mutations reflect the somatic evolutionary process, and thus, it has been conjectured, the aging status of the body. Such a timer has been impractical thus far, however, because detection of somatic variants in single cells presents a significant technological challenge. Here, we show that somatic mutations detected using single-cell RNA sequencing (scRNA-seq) from thousands of cells can be used to construct a cell lineage tree whose structure correlates with chronological age. De novo single-nucleotide variants (SNVs) are detected in human peripheral blood mononuclear cells using a modified protocol. A default model based on penalized multiple regression of chronological age on 31 metrics characterizing the phylogenetic tree gives a Pearson correlation of 0.81 and a median absolute error of similar to 4 years between predicted and chronological ages. Testing of the model on a public scRNA-seq dataset yields a Pearson correlation of 0.85. In addition, cell tree age predictions are found to be better predictors of certain clinical biomarkers than chronological age alone, for instance glucose, albumin levels, and leukocyte count. The geometry of the cell lineage tree records the structure of somatic evolution in the individual and represents a new modality of aging timer. In addition to providing a numerical estimate of "cell tree age," it unveils a temporal history of the aging process, revealing how clonal structure evolves over life span. Cell Tree Rings complements existing aging clocks and may help reduce the current uncertainty in the assessment of geroprotective trials.