A dispensing cap and a container having a dispensing cap are provided in which the dispensing cap includes first and second parts designed for mounting onto a container. The dispensing cap includes: (a) a first part fitted with an interior output orifice suitable for allowing selective communication with the container interior; and (b) a second part through a conduit extends and which opens at a dispensing outlet. The second part is arranged so that it can rotate on axis Y, which is aligned obliquely to an axis X of the container, in such a way as to move from a closed position at which the second part will seal off the interior output orifice to a dispensing position in which the interior output orifice will communicate with the dispensing outlet by way of the conduit. In addition, the dispensing cap is configured in such a way as to activate a dispensing member provided on the container.