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 ends when the viral nucleic acid is released into the host cytoplasm when the viral membrane fuses with the endosomal membrane.