  We study percolation transition of run and tumble particles (RTPs) on a two
dimensional square lattice. RTPs in these models run to the nearest neighbour
along their internal orientation with unit rate, and to other nearest
neighbours with rates $p$. In addition, they tumble to change their internal
orientation with rate $\omega$. We show that for small tumble rates,
RTP-clusters created by joining occupied nearest neighbours irrespective of
their orientation form a phase separated state when the rate of positional
diffusion $p$ crosses a threshold; with further increase of $p$ the clusters
disintegrate and another transition to a mixed phase occurs. The critical
exponents of this re-entrant site-percolation transition of RTPs vary
continuously along the critical line in the $\omega$-$p$ plane, but a scaling
function remains invariant. This function is identical to the corresponding
universal scaling function of percolation transition observed in the Ising
model. We also show that the critical exponents of the underlying motility
induced phase separation transition are related to corresponding
percolation-critical-exponents by constant multiplicative factors known from
the correspondence of magnetic and percolation critical exponents of Ising
model.
