Yes, gravity does cause relativistic effects, including time dilation. According to the theory of general relativity, gravity is not just a force but is instead a curvature of spacetime caused by mass and energy.
In the presence of a gravitational field, clocks located at different positions experience differences in the flow of time. This effect is known as gravitational time dilation. The closer a clock is to a massive object or the stronger the gravitational field it is in, the slower time passes for that clock compared to a clock located in a weaker gravitational field or further away from massive objects.
This gravitational time dilation can be observed and has been verified experimentally. For example, atomic clocks placed at different altitudes or in orbit around the Earth show measurable differences in their tick rates due to the variation in gravitational field strength.
Furthermore, extreme gravitational fields, such as those near black holes, can cause significant time dilation effects. Near the event horizon of a black hole, where gravity is extremely strong, time dilation becomes so extreme that it can lead to phenomena like time appearing to stand still for an outside observer, while time proceeds normally for an object falling into the black hole.
In summary, gravity does cause relativistic effects, including time dilation. The presence of a gravitational field leads to variations in the flow of time, with time passing more slowly in stronger gravitational fields compared to weaker ones.