Abstract Background Cervical cancer remains the second most common cause of death in women and poses a growing public health challenge. It is urgent to increase cervical cancer screening rates in Kenya as per the 2018 Kenya National Cancer Screening Guidelines. Addressing access to care may serve as a target to achieve this goal; however, how individual dimensions of access to care are associated with the utilization of cervical cancer screening services in low- and middle-income countries, including Kenya, remains unclear. This study aimed to examine how different aspects of access to care (affordability, availability, geographical access, and social influence) were associated with cervical cancer screening among Kenyan women of reproductive age. Methods This cross-sectional study used data from the 2014 Kenya Demographic and Health Survey and the 2010 Kenya Service Provision Assessment. The final sample included 5,563 women aged 25–49 years. Logistic regression models were used to examine the association between different aspects of access to care and the uptake of cervical cancer screening. Results Factors such as being in the poorest wealth quintile, lacking health insurance, having difficulty obtaining funds for treatment (affordability), limited availability of screening services at nearby facilities (availability), living in rural areas (geographical access), and having healthcare decisions made solely by husbands/partners or others (social influence) were associated with a decreased likelihood of the uptake of cervical cancer screening. Conclusions Increasing health insurance coverage, enhancing the availability of screening services at health facilities, expanding mobile screening health facilities in rural areas, and empowering women to make their own healthcare decisions are crucial steps for increasing cervical cancer screening uptake in Kenya.