High-quality integrated diamond photonic devices have previously been demonstrated in applications from non-linear photonics to on-chip quantum optics. However, the small sample sizes of single crystal material available, and the difficulty in tuning its optical properties, are barriers to the scaling of these technologies. Both of these issues can be addressed by integrating micrometer-scale diamond devices onto host photonic integrated circuits using a highly accurate micro-assembly method. In this work a diamond micro-disk resonator is integrated with a standard single-mode silicon-on-insulator waveguide, exhibiting an average loaded $Q$-factor of $3.1\times {10}^4$ across a range of spatial modes, with a maximum loaded $Q$-factor of $1.05\times {10}^5$. The micrometer-scale device size and high thermal impedance of the silica interface layer allow for significant thermal loading and continuous resonant wavelength tuning across a 450 pm range using a milliwatt-level optical pump. This diamond-on-demand integration technique paves the way for tunable devices coupled across large-scale photonic circuits.