  A number of nuclear decay anomalies have been reported in the literature,
which purport to show periodic variations in the decay rates of certain
radioisotopes. If these reports reflect reality, they would necessitate a
seismic shift in our understanding of fundamental physics. We provide the first
mechanism to explain these findings, via the misalignment mechanism of QCD
axion dark matter, wherein oscillations of the effective $\theta$ angle induce
periodic variation in nuclear binding energies and hence decay rates. As we
expect this effect to be most pronounced in low-$Q$ systems, we analyse 12
years of tritium decay data ($Q\simeq$ 18.6 keV) taken at the European
Commission's Joint Research Centre. Finding no statistically significant
excess, we exclude axion decay constants below $9.4\times10^{12} -
1.8\times10^{10}$ GeV (95% confidence level) for masses in the
$1.7\times{10}^{-23} - 8.7\times 10^{-21}$ eV range.
