Is there any relation between inclination of injected orbit and the launch site ?
Yes. While you can change your inclination over a burn, in a classic "plain" launch your starting latitude is the inclination peaks where your orbit is directly above them relative to the launch site location. If you launch from Cape Canaveral and go "straight" from it with no immediate major change in longitude, the antipode will be the opposite coordinates, so 30°N is 30° south. And if you do have a change in longitude it makes your orbit even more inclined. If you do an inclination changing burn in ascent you can avoid any major inclination from launch sites' latitudes.
For a direct injection into orbit (i.e. no dog leg later), then by simple geometry, the orbit inclination will be greater than or equal to the absolute value of the latitude of the location of that injection, which is very close to the latitude of the launch site. A launch azimuth of zero (due East or due West) would result in an inclination equal to the latitude.
There may be further constraints on the inclination due to the allowed launch azimuth to avoid overflight of populated areas, or to provide telemetry coverage with available downtrack ground stations.