As the heaviest known fundamental particle, the top quark ensures testing of the Standard Model and occupies a significant role in a lot of theories of new physics beyond the Standard Model. Up to now, the top quark has been only generated at the Tevatron and the Large Hadron Collider. However, one of the most important tasks of the physics program at the Large Hadron Collider is the investigation of the anomalous top quark interactions. In addition, the production of single top quarks, though rarer than production in pairs, presents us a different way to study the top quark produced via the electroweak interaction. This makes single top quark production an important signature for studying the properties of the top quark. Hence, we examine the anomalous tt gamma interactions to investigate limits on the anomalous a(A) and a(V) couplings through single top quark production of the process pp -> p gamma*p -> ptWX at the Large Hadron Collider, the High Luminosity Large Hadron Collider and High Energy Large Hadron Collider. The best limits obtained on the anomalous a(A) and a(V) couplings through the subprocess gamma*b -> Wt at the High Energy Large Hadron Collider with L-int = 15 ab(-1) at 68% Confidence Level are found to be vertical bar a(A)vertical bar = 0.0509 and a(V) = [-0.3171; 0.0077]. Therefore, we understand that gamma*p collisions at the High Energy Large Hadron Collider improves the sensitivity limits of the anomalous coupling parameters according to previous studies. (C) 2020 The Author(s). Published by Elsevier B.V.