  We investigate the effect of initial conditions on the fluctuations of the
integrated density current across the origin ($x=0$) up to a given time $t$ in
a one-dimensional system of non-interacting run-and-tumble particles. Each
particle has initial probabilities $f^+$ and $f^-$ to move with an initial
velocity $+v$ and $-v$ respectively, where $v>0$. We derive exact results for
the variance (second cumulant) of the current for quenched and annealed
averages over the initial conditions for the magnetization and the density
fields associated with the particles. We show that at large times, the variance
displays a $\sqrt{t}$ behavior, with a prefactor contingent on the specific
density initial conditions used. However, at short times, the variance displays
either linear $t$ or quadratic $t^2$ behavior, which depends on the combination
of magnetization and density initial conditions, along with the fraction $f^+$
of particles in the positive velocity state at $t=0$. Intriguingly, if $f^+=0$,
the variance displays a short time $t^2$ behavior with the same prefactor
irrespective of the initial conditions for both fields.
