Strategic classification studies the design of a classifier robust to the manipulation of input by strategic individuals. However, the existing literature does not consider the effect of competition among individuals as induced by the algorithm design. Motivated by constrained allocation settings such as college admissions, we introduce strategic ranking, in which the (designed) individual reward depends on an applicant's post-effort rank in a measurement of interest. Our results illustrate how competition among applicants affects the resulting equilibria and model insights. We analyze how various ranking reward designs, belonging to a family of step functions, trade off applicant, school, and societal utility, as well as how ranking design counters inequities arising from disparate access to resources. In particular, we find that randomization in the reward design can mitigate two measures of disparate impact, welfare gap and access.