1. The Deathstar doesn't orbit anything, it's a free moving spaceship so most of the time, no.
2. The deathstar is not as dense as a moon since its has many empty internal cavities while a moon is solid, therefore it is less dense then a real moon and has less gravitational pull.
3. Moons come in various sizes, some of which are very small. It's never noted whither the Deathstar looks like a big moon or a small moon. If its a small ,oon, it could have little to no affect on tides.
Really what matters is actual how much mass the Dethstar has. It it has sufficient mass, and if for some reason it was orbiting a planet (a stationary deathstar would only create one continuous tide on the plant) then it could create a tide. However unless some band of rouge Stormtroopers takes the Deathstar for a joyride, it most likely wouldn't be orbiting anything and we'd never know.