Mood disorders, including depression and anxiety, affect almost one-fifth of the world’s adult population and are becoming increasingly prevalent. Mutations in circadian clock genes have previously been associated with mood disorders both directly and indirectly through alterations in circadian phase, suggesting that the circadian clock influences multiple molecular pathways involved in mood. By targeting previously identified single nucleotide polymorphisms (SNPs) that have been implicated in anxiety and depressive disorders, we use a combination of statistical and machine learning techniques to investigate associations with the generalized anxiety disorder assessment (GAD-7) scores in a UK Biobank sample of 90,882 individuals. As in previous studies, we observed that females exhibited higher GAD-7 scores than males regardless of genotype. Interestingly, we found no significant effects on anxiety from individual circadian gene variants; only circadian genotypes with multiple SNP variants showed significant associations with anxiety. For both sexes, severe anxiety is associated with a 120-fold increase in odds for individuals with CRY2_AG(rs1083852)/ZBTB20_TT(rs1394593) genotypes and is associated with a near 40-fold reduction in odds for individuals with PER3-A_CG(rs228697)/ZBTB20_TT(rs1394593) genotypes. We also report several sex-specific associations with anxiety. In females, the CRY2/ZBTB20 genotype combination showed a > 200-fold increase in odds of anxiety and PER3/ZBTB20 and CRY1 /PER3-A genotype combinations also appeared as female risk factors. In males, CRY1/PER3-A and PER3-B/ZBTB20 genotype combinations were associated with anxiety risk. Mediation analysis revealed direct associations of CRY2/ZBTB20 variant genotypes with moderate anxiety in females and CRY1/PER3-A variant genotypes with severe anxiety in males. The association of CRY1/PER3-A variant genotypes with severe anxiety in females was partially mediated by extreme evening chronotype. Our results reinforce existing findings that females exhibit stronger anxiety outcomes than males, and provide evidence for circadian gene associations with anxiety, particularly in females. Our analyses only identified significant associations using two-gene combinations, underscoring the importance of combined gene effects on anxiety risk. We describe novel, robust associations between gene combinations involving the ZBTB20 SNP (rs1394593) and risk of anxiety symptoms in a large population sample. Our findings also support previous findings that the ZBTB20 SNP is an important factor in mood disorders, including seasonal affective disorder. Our results suggest that reduced expression of this gene significantly modulates the risk of anxiety symptoms through direct influences on mood-related pathways. Together, these observations provide novel links between the circadian clockwork and anxiety symptoms and identify potential molecular pathways through which clock genes may influence anxiety risk.