Autism spectrum disorder and anxiety are highly comorbid conditions. Understanding the underlying traits of anxiety in autism spectrum disorder is crucial to prevent and treat it efficiently. Hence, this study determined whether social communication difficulties or restricted repetitive behaviors are stronger risk factors for anxiety symptoms in autistic adults in a large cohort. Data on 742 autistic adults from the Netherlands Autism Register were included in the study. Hierarchical regression was implemented to evaluate whether social communication difficulties (Autism-Spectrum Quotient social behavior factor) and restricted repetitive behaviors (Adult Routines Inventory) were predictive of anxiety (Hospital Anxiety and Depression Scale) controlling for age and sex. When considered together, restricted repetitive behaviors stood out as significant positive predictors of anxiety symptoms (lower-order restricted repetitive behaviors, β = 0.32, p < 0.001; higher-order restricted repetitive behaviors, β = 0.15, p = 0.001), whereas social communication difficulties did not (β = 0.06, p = 0.11). Sex did not moderate these associations (p > 0.05). Non-social autistic traits are stronger predictors of anxiety symptoms than social traits in autistic adults. Increased attention to restricted repetitive behaviors should be given to improve current support programs for autistic adults with anxiety and to identify autistic individuals at risk.