Cognitive performance is significantly affected by sleep, but mild chronic sleep deprivation in daily life remains difficult to measure. Laboratory-enforced sleep restriction may not fully replicate real-life conditions. This study investigates whether Social Jet Lag (SJL), an indicator of misalignment between biological and social time, can used as a proxy for mild chronic sleep deprivation and its impact on cognitive function. Participants leading typical social lives were selected based on their SJL scores, and cognitive performance was assessed using an online experiment incorporating a Psychomotor Vigilance Task (PVT) and a Sustained Attention to Response Task (SART) at different times (post-wake and pre-sleep) and across multiple days (Sunday, Monday, and Friday). Generalised linear modelling (GLM) revealed that SJL was consistently the most explanatory factor for cognitive performance, while test timing also had a significant impact. Cognitive performance impairments due to SJL remained stable across days, suggesting a stable influence of sleep timing irregularity. Additionally, SJL was associated with increased false-positive rates in the SART, indicating reduced response inhibition ability. While SJL proved to be a useful measure compared to average sleep duration and the Sleep Regularity Index (SRI), its effectiveness may be specific to populations following structured work schedules.