Can we conclude that electric current is also a reference dependent quantity?
yes. Electric current density forms part of a four-vector whose timelike component is the electric charge density, in the same way that momentum forms the spacelike part of a four-vector whose timelike component is energy.
In other words, $j^\mu = (\rho,\vec j)$ is a four-vector and transforms as such under Lorentz frame transformations. Among other things, this entails that
- the charge density mixes into the current, i.e. a stationary charge produces an electric current when seen from a reference frame where the charge is moving (a fact which is not at all surprising, but)
- if a neutral configuration with nonzero currents is seen from an appropriate reference frame, then a net charge density will appear.
This last bit is pretty surprising, and it is not expected from classical kinematics: a stationary test charge won't feel a force from a neutral set of currents, but a moving test charge will feel a force (which, by continuity, must be proportional to the velocity, at least at low $v$). Or, in other words, it sees a magnetic field.
For more details on that connection, I recommend the relativity chapters at the start of Ed Purcell's Electricity and Magnetism.