Electrical connector for an apparatus for charging electric storage battery cells, which comprises: - a bush made of conductive material, which is susceptible of being power supplied by an electrical power source, is provided with an internal cavity delimited by a substantially flat end wall, a bottom wall and a first lateral wall of the bush, said end wall being susceptible of abutting against, by means of a contact surface thereof, an electrode of a cell of an electric storage battery, in order to electrically charge it; - at least one electrical contacting element made of conductive material, mounted inside said bush, susceptible of being connected to measurement means and of abutting against, by means of a free end thereof, the electrode of said cell, in order to carry out electrical measurements; wherein said electrical contacting element comprises: - a common base electrically connected to a cable of said measurement means; - a plurality of pins, which are extended, parallel to each other, starting from said common base; - electrical isolation means, which are housed within the cavity of said bush in order to electrically isolate said bush from said electrical contacting element; said electrical connector being characterized in that the pins of said electrical contacting element traverse a corresponding plurality of through holes made on said end wall and are susceptible of projecting from said contact surface, with the free end thereof; wherein said electrical connector comprises first elastic means, which are housed within the internal cavity of said bush and act against said electrical contacting element for pushing the free ends of said pins outside the contact surface of said end wall; wherein said electrical isolation means comprise a first isolation body provided with: - a base element interposed between the common base of said contacting element and the internal face of the end wall of said bush; and - a plurality of tubular elements which are connected to said base element and are inserted in the through holes of said end wall in order to isolate said pins from said bush. - a bush made of conductive material, which is susceptible of being power supplied by an electrical power source, is provided with an internal cavity delimited by a substantially flat end wall, a bottom wall and a first lateral wall of the bush, said end wall being susceptible of abutting against, by means of a contact surface thereof, an electrode of a cell of an electric storage battery, in order to electrically charge it; - at least one electrical contacting element made of conductive material, mounted inside said bush, susceptible of being connected to measurement means and of abutting against, by means of a free end thereof, the electrode of said cell, in order to carry out electrical measurements; - a common base electrically connected to a cable of said measurement means; - a plurality of pins, which are extended, parallel to each other, starting from said common base; - electrical isolation means, which are housed within the cavity of said bush in order to electrically isolate said bush from said electrical contacting element; - a base element interposed between the common base of said contacting element and the internal face of the end wall of said bush; and - a plurality of tubular elements which are connected to said base element and are inserted in the through holes of said end wall in order to isolate said pins from said bush.