Blotting paper absorbs ink due to

Blotting paper absorbs ink by the process of capillary action. The capillary action is based on the property of surface tension of liquid.
All unsized paper will absorb water. Blotting paper is not sized and made bulkier to provide capillary action for faster absorption of liquid.
Blotting paper has also been sold as a cosmetic to aid in the removal of skin oils and makeup.