  Rotating black hole solutions in theories of modified gravity are important
as they offer an arena to test these theories through astrophysical
observation. The non-rotating black hole can be hardly tested since the black
hole spin is very important in any astrophysical process. We present rotating
counterpart of a recently obtained spherically symmetric exact black hole
solution surrounded by perfect fluid in the context of Rastall theory, viz,
rotating Rastall black hole that generalize the Kerr-Newman black hole
solution. In turn, we analyze the specific cases of the Kerr-Newman black holes
surrounded by matter like dust and quintessence fields. Interestingly, for a
set of parameters and a chosen surrounding field, there exists a critical
rotation parameter ($a=a_{E}$), which corresponds to an extremal black hole
with degenerate horizons, while for $a<a_{E}$, it describes a non-extremal
black hole with Cauchy and event horizons, and no black hole for $a>a_{E}$ with
value $a_E$ is also influenced by these parameters. We also discuss the
thermodynamical quantities associated with rotating Rastall black hole, and
analyze the particle motion with the behavior of effective potential.
