(1) Background: Worldwide, refugees may have some difficulties in accessing healthcare services. However, little is known about the factors that may predict the level of accessibility to the public healthcare system in the host countries. (2) Aim: To examine the level of accessibility of Syrian refugees to the public healthcare system in Jordan and further to identify the prediction of socioeconomic factors and barriers to healthcare access. (3) Methods: A cross-sectional study was conducted with a convenient sample of 356 Syrian refugees residing outside camps (Irbid, Ajloun, and Jarash). Data were collected using the Access to Healthcare Services Scale instrument (adopted from the Canadian Community Health Survey), which is composed of 2 sections: the general access scale (8 items) and the difficulties scale (20 items). One-way ANOVA test and independent t-test were used to examine epidemiological correlations among variables, whereas a hierarchical linear regression model was used to examine the predictability of socioeconomic factors and barriers to overall access to the public healthcare system by exploring the incremental impact of additional predictors. (4) Results: the mean age of the 356 participants was 35.22 years old, 56.5% were female, 67.4% were married, most of them 46.1% have secondary education, and non-employed 69.9%. Significant associations were observed among participants with different marital status (p < 0.001), educational level (mean 11.85 vs. 19.85, p < 0.001), working status (15.47 vs. 17.93, p < 0.001), family household number (16.42 vs. 17.0, p < 0.001), and health insurance (none: 15.50 vs. governmental 24.50, p < 0.001). Multivariate analysis revealed that the most important factors that may predict the overall access to healthcare services were: family monthly income (beta −0.19, p < 0.001), household family number (beta 0.17, <0.001), health insurance (beta −0.09, p = 0.047), and barriers (beta −0.43, <0.001), even after adjusting for potential confounding effects: sex, age, educational level, and place of residence. (5) Conclusions: Our findings indicate that socioeconomic factors and barriers may considerably predict overall access to public healthcare in Jordan. It is crucially important, therefore, for the Jordanian government and international organizations to create and develop strategic plans and programs that enhance refugees’ access to health services, positively impacting their health and wellness.