In the present work we study non-rotating dark stars in $f(R)$ modified theory of gravity. In particular, we have considered bosonic self-interacting dark matter modelled inside the star as a Bose-Einstein condensate, while as far as the modified theory of gravity is concerned we have assumed Starobinsky's model $R+aR^2$. We solve the generalized structure equations numerically, and we obtain the mass-to-ratio relation for several different values of the parameter $a$, and for two different dark matter equation-of-states. Our results show that the dark matter stars become more compact in the R-squared gravity compared to General Relativity, while at the same time the highest star mass is slightly increased in the modified gravitational theory. The numerical value of the highest star mass for each case has been reported.

6 pages, 2 tables, 3 figures, to appear in PRD