It is reported in the present invention a device (A) to monitor the tension on an anchoring line (LA) of a floating platform for oil exploration or production at sea, which is mounted at a point on the anchoring line without it becoming an integral part thereof, which basically comprises: an upper bar (1) and a lower bar (2), which are interconnected at one end by a hydraulic cylinder (CH1) and on the other end by a solid vertical bar (4).