Can a plane land on a full tank of fuel?

Some can, some can't. Larger air-transport category aircraft have a maximum landing weight limitation. If enough passengers, baggage and fuel are aboard, the plane could be over the limit. If the plane could not complete the trip, perhaps because of weather, it would have to circle around, burning fuel, until the weight was low enough. In an emergency, the plane would dump fuel overboard to lower the weight. This situation generally happens on long flights where the plane is in the air many hours and thus requires a large fuel load, such as on trans-oceanic flights The limitation is not whether the tank is full or not, but total weight. The same aircraft with full fuel and no passengers might be legal to land with no problems. Smaller aircraft actually have the opposite problem. If they are overweight, there is not enough power to take off. If they are light enough to take off, they are light enough to land. So the precice answer to your question depends on the model of aircraft and the additional weight of passengers and baggage.