We propose a scalable synaptic circuit realizing spike timing dependent plasticity (STDP)-compatible with randomly spiking neurons. The feasible working of the circuit was examined by circuit simulation using the BSIM 4.6.0 model. A distinguishable feature of the circuit is the use of floating-gate integrators that provide the compact implementation of biologically plausible relaxation time scale. This relaxation occurs on the basis of charge tunneling that mainly relies upon area-independent tunnel barrier properties (e.g. barrier width and height) rather than capacitance. The circuit simulations feature (i) weight-dependent STDP that spontaneously limits the synaptic weight growth, (ii) competitive synaptic adaptation within both unsupervised and supervised frameworks with randomly spiking neurons. The estimated power consumption is merely 34 pW, perhaps meeting one of the most crucial principles (power-efficiency) of neuromorphic engineering. Finally, a means of fine-tuning the STDP behavior is provided.