Modular soft robots have the advantage in their ability to be reconfigured and change their morphology on-demand according to a specified task. The actuator design and particularly the inter-unit connectivity strength commonly govern the usability and functionality of these modular robots and their applications. In this paper, we present development of reconfigurable modular rotary soft actuators that allow the construction of highly versatile soft robotic actuators and systems. These pneumatically driven modular actuators are composed of an inner balloon and a flexible arched reinforcement structure to produce a rotary motion. They serve as building blocks which may be combined in various configurations to construct linear assemblies capable of extensile or bending motions. The connection scheme allows for the larger actuators to grow or shrink with the addition or removal of modules. Using finite element simulations and physical characterizations, we systematically explore the mechanical response of individual modular actuators and the role of various connection schemes on their motions upon pressurization. A key conceptual contribution of this work lies in the idea that for a modular soft robotic system, offsetting and tuning actuator alignment relative to an axis of symmetry can lead to substantial changes in mechanical performance. Utilizing these modules we demonstrate the reconfigurability of this modular system by both reconfiguring a large actuator into a pair of smaller actuators that can grasp delicate objects, and reconfiguring actuators to develop a linear crawling robot.