When a convergent boundary collides, subduction occurs and the denser crust that slides underneath the lighter crust is recycled into the mantel. This makes fuel for volcanic eruptions.
The newly fulled volcano erupts, and causes degassing. Degassing is when carbon dioxide is released into the air because it is unstable and under pressure.
The carbon dioxide is released into the atmosphere, causing a greenhouse effect. This makes the global temperature warmer.
The most noticeable example of the relationship between plate tectonics and the carbon cycle is the breakup of Pangaea.
After Pangaea broke up, the small continents were surrounded by moisture. The increased moisture led to an abundance of rainfall. This took the carbon dioxide out of the atmosphere. However, this carbon-dioxide-filled rain sped up the process of errosion.
The reduction of greenhouse gasses in the atmosphere led to global cooling. More glaciers formed, and they reflected the solar energy, perpetuating the cycle of global cooling.
The excessive cold led to dry air, which eventually stopped glacial growing. Deserts were created, there was no rainfall, and the carbon dioxide stayed in the atmosphere. This started the greenhouse affect again.