Due to the forces of adhesion, cohesion, and surface tension, capillary action is explained as the movement of the liquid which occurs due to the difference in cohesive and adhesive forces.
Here, it appears due to the sticky nature of liquid ink.
The life examples of capillary action are falling the liquids between the hairs of the paintbrush, liquids flow in biological cells and flow in a thin tube.
Blotting paper is an thin and smooth material that allows a little thicker liquids like ink to absorb.
When blotting paper is dipped in ink, the ink rises up the paper due to capillary rise Hence, the absorption of ink by blotting paper involves the capillary action process.