In contrast to the popular multimode orbital angular momentum (OAM) generation method that uses uniform circular array combined with phase shifter network, time-modulated circular array (TMCA) does not require multiple radio frequency chains and costly analog devices and it requires only switches. In this article, an arbitrary-order OAM generation and beam steering method for TMCA is proposed, which incorporates the existing integer-order OAM generation and beam steering method as a special case. Furthermore, we analyze the effect of elements <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</small> – <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">off</small> ordering on the generation of OAM beams, and prove that sequential ordering has the lowest power consumption. Finally, the effectiveness of the proposed methods is validated through electromagnetic simulations.