  We study the Floquet amorphous topological orders in experimentally
accessible one-dimensional array of randomly pointed Rydberg atoms with
periodic driving. The filling factor in the chain is tunable by applying a
microwave field. We give a complete characterization of the topological
properties from both the single-particle and many-body aspect. The periodic
driving results in richer topological phases. At the single-particle level, we
calculate the real space winding numbers and polarization, confirming robust
amorphous topological phases with 0-type and $\pi$-type edge modes. We show a
structural disorder induced topological phase transition acompanied with
localization transition in the nonequilibrium system. Furthermore, in the
many-body case we find the existence of amorphous topological orders of the
hardcore bosons half-filled the chain, in contrast described by the topological
entanglement entropy and the string order. Possible detection methods are also
addressed.
