Usually, but not always. For instance, if the film is not smooth, then what is it's thickness? If a film is very thin, then it may have pinholes, or voids. A thick film can often have protrusions. Both voids and protrusions make it difficult to know the average film thickness. Also, if a film is under a great deal of stress, then its possible for its mass density to be somewhat decreased. However, for most metals, the film density will be nearly the same as the bulk density.

For an ideally homogeneous, ultra smooth film, the film mass per unit area m_A, thickness t, and density \rho are related as you might expect by m_A = t * \rho. When the film is porous, a first approximation might be to include porosity f_p as \rho_p = (1 - f_p)*\rho where \rho_p is the density of the porous film. As the film becomes less than ultra-smooth (surface roughness), additional considerations are warranted. Finally, if the film is inhomogeneous in its composition, further corrections may have to be made.

I like each of the earlier answers! Very good.

But shouldn't we refer Umut, the OP (original posting member) to the literature on structure zone diagrams? I mean the Movchan and Demchishin diagram, the Thornton diagram, etc. The density versus thickness for thin metal films may not change very much, in terms of percentage deviation from the accepted bulk value, but these small changes include a world of complexity that affect properties very much. The microstructural details, and hence properties, may depend very much on the exact sputter deposition conditions, as well as upon substrate identity, surface preparation, post-treatment and trace impurities.

The most recent paper on SZDs I know of is a great one for this OP. It is:

André Anders, "A structure zone diagram including plasma-based deposition and ion etching", Thin Solid Films 518, 4087–4090 (2010). I think Dr. Anders may have uploaded it already to RG. This paper is not only a pretty thorough review of all historical zone diagrams but also introduces the effects of energetic heavy particles, which may or may not be relevant in the OP's sputtering apparatus.