The relationship between skeletal muscle and cognitive disorders has drawn increasing attention. This study aims to examine the associations of sarcopenia with cognitive function and dementia risk score. Data on 1978 participants (aged 65 years and older) from the 2011 wave of the China Health and Retirement Longitudinal Study, with four follow-up waves to 2018, were used. Cognitive function was assessed by four dimensions, with a lower score indicating lower cognitive function. Dementia risk was assessed by a risk score using the Rotterdam Study Basic Dementia Risk Model (BDRM), with a higher score indicating a greater risk. Sarcopenia was defined when low muscle mass plus low muscle strength or low physical performance were met. We used generalized estimating equations to examine the associations of sarcopenia. In the fully adjusted models, sarcopenia was significantly associated with lower cognitive function (standardized, β = −0.15; 95% CIs: −0.26, −0.04) and a higher BDRM score (standardized, β = 0.42; 95% CIs: 0.29, 0.55). Our findings may provide a new avenue for alleviating the burden of cognitive disorders by preventing sarcopenia.