The uptake of a virus into a host cell that begins by invagination of a specific region of the host cell plasma membrane around the bound virus to form a clathrin-coated pit, which then pinches off to form a clathrin-coated endocytic vesicles containing the virus. The vesicle then delivers its viral content to early endosomes, and the process ends when viral nucleic acid is released into the host cytoplasm by induction of endosome membrane permeabilization triggered by an interaction between the host membrane and a membrane-penetration protein associated with the capsid.