The main goal of this paper is to investigate one of the important
    astrophysical systems, namely Thick accretion disks, in the background of the
    spherically symmetric solution in Born-Infeld teleparallel gravity to examine
    observable predictions of the theory in the vicinity of black holes. Thus, the
    properties of the non-self-gravitating equilibrium surfaces characterising the
    Thick accretion disks model are studied. In addition, we find an observational
    bound on the parameter of the model as $\lambda\gtrsim 140$. We show this
    analytical accretion disk model for different values of $\lambda$ and compare
    the result with the corresponding Schwarzschild solution in the general theory
    of relativity.

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