Parents of children with Autism Spectrum Disorder (ASD) are more likely to exhibit subclinical autistic characteristics, commonly described as the Broad Autism Phenotype (BAP). This study examines whether the WAIS-R verbal-performance discrepancy and total range scores are associated with social skill deficits in parents of children with ASD, considering sex differences. This case–control study included 24 parents of children with ASD without psychopathology and 28 healthy controls. Participants underwent a structured diagnostic interview (SCID-5-CV) and completed the Autism Spectrum Quotient (AQ). Verbal, performance and total range scores were calculated based on the difference between the highest and lowest subtest scores. Parents of children with ASD exhibited significantly higher AQ social skills subscale and total scores than controls. Fathers had significantly higher verbal range scores than controls, whereas no significant differences were found in mothers. Logistic regression revealed that each 1-point increase in verbal range was associated with a 55.7% higher likelihood (p = 0.032) of belonging to the ASD-parent group among fathers. An optimal cut-off score of 7.5 was identified, with 58.3% sensitivity and 71.4% specificity for distinguishing fathers in the ASD-parent group from controls. Verbal IQ range may represent a potential cognitive marker associated with BAP traits, particularly social skill difficulties, in fathers of children with ASD. However, larger studies are needed to further clarify its clinical significance.