Alcohol dependence is frequently co-morbid with cognitive impairment. The relationship between these traits is complex as cognitive dysfunction may arise as a consequence of heavy drinking or exist prior to the onset of dependence. In the present study, we tested the genetic overlap between cognitive abilities and alcohol dependence using polygenic risk scores (PGRS). We created two independent PGRS derived from two recent genome-wide association studies (GWAS) of alcohol dependence (SAGE GWAS: n = 2750; Yale-Penn GWAS: n = 2377) in a population-based cohort, Generation Scotland: Scottish Family Health Study (GS:SFHS) (n = 9863). Data on alcohol consumption and four tests of cognitive function [Mill Hill Vocabulary (MHV), digit symbol coding, phonemic verbal fluency (VF) and logical memory] were available. PGRS for alcohol dependence were negatively associated with two measures of cognitive function: MHV (SAGE: P = 0.009, β = −0.027; Yale-Penn: P = 0.001, β = −0.034) and VF (SAGE: P = 0.0008, β = −0.036; Yale-Penn: P = 0.00005, β = −0.044). VF remained robustly associated after adjustment for education and social deprivation; however, the association with MHV was substantially attenuated. Shared genetic variants may account for some of the phenotypic association between cognitive ability and alcohol dependence. A significant negative association between PGRS and social deprivation was found (SAGE: P = 5.2 × 10−7, β = −0.054; Yale-Penn: P = 0.000012, β = −0.047). Individuals living in socially deprived regions were found to carry more alcohol dependence risk alleles which may contribute to the increased prevalence of problem drinking in regions of deprivation. Future work to identify genes which affect both cognitive impairment and alcohol dependence will help elucidate biological processes common to both disorders.