Telescope array receiver is a viable architecture for Earth-based reception in a deep-space optical communication system. In this paper, effects of random tracking errors on the performance of optical array receivers for an inter-planetary deep-space optical communications link between Earth and Mars is investigated. The paper has two major parts. In the first part, statistical analysis and mathematical modeling of the impact of tracking errors on general direct-detection optical communication receivers is presented. The analytical results show that tracking errors could severely degrade the performance of optical receivers; hence, these need to be compensated, especially in a deep-space link. In the second part, design and analysis of a closed-loop tracking subsystem for telescope array receivers operating in a deep-space link is presented. An end-to-end simulation platform for communication between Earth and Mars is implemented that incorporates direct-detection array receivers and the proposed tracking subsystems to alleviate the effects of random tracking errors. Extreme channel conditions, i.e., maximum distance, strong background noise and turbulence conditions are modeled to evaluate the performance bounds. Simulations results depict that in worst-case channel conditions, the proposed architecture mitigates the impact of tracking errors to be within reasonable limits. Comparison of achievable data rates show that in the presence of random tracking errors, replacement of a large telescope (10m diameter) with an array of relatively smaller-sized telescopes (i.e., 100, 1m telescopes) results in acceptable performance loss (i.e., <13%). Hence, performance degradation due to tracking errors does not pose a major limitation in employing array architecture in deep-space communication. The presented analysis further strengthens the viability of array architecture compared to a monolithic, large telescope for deep-space communications.