The expansion of augmented reality across society, its availability in mobile platforms and the novelty character it embodies by appearing in a growing number of areas, have raised new questions related to people’s predisposition to use this technology in their daily life. Acceptance models, which have been updated following technological breakthroughs and society changes, are known to be great tools for predicting the intention to use a new technological system. This paper proposes a new acceptance model aiming to ascertain the intention to use augmented reality technology in heritage sites—the Augmented Reality Acceptance Model (ARAM). ARAM relies on the use of the Unified Theory of Acceptance and Use of Technology model (UTAUT) model’s constructs, namely performance expectancy, effort expectancy, social influence, and facilitating conditions, to which the new and adapted constructs of trust expectancy, technological innovation, computer anxiety and hedonic motivation are added. This model was validated with data gathered from 528 participants. Results confirm ARAM as a reliable tool to determine the acceptance of augmented reality technology for usage in cultural heritage sites. The direct impact of performance expectancy, facilitating conditions and hedonic motivation is validated as having a positive influence on behavioural intention. Trust expectancy and technological innovation are demonstrated to have a positive influence on performance expectancy whereas hedonic motivation is negatively influenced by effort expectancy and by computer anxiety. The research, thus, supports ARAM as a suitable model to ascertain the behavioural intention to use augmented reality in new areas of activity.