Is it possible to produce virtual gravity? I mean gravity without the help of mass by curving spacetime with other effects like fast rotating objects?
The source of the curvature that leads to gravitation is an object called the stress-energy tensor. This does include mass, or more precisely energy, but it also includes other sources for gravity such as momentum flow, shear stress and pressure. It's been suggested there could be objects called geons where the energy of the gravitational field acts as a source for the gravitational field, so no mass is present, but these are still hypothetical.
A quick edit in the light of twistor59's comment: massless objects like photons can generate a gravitational field because mass and energy are related by the famous equation $E = mc^2$ so from a gravitational point of view energy behaves like mass. In fact the stress-energy tensor includes just one entry for combined mass and energy.
But I would guess you are asking if we can generate gravity from sources that don't appear in the stress-energy tensor. According to General Relativity the answer is no, though over the years various people have claimed to see effects. For example Eugene Podkletnov has claimed to gravitational effects from rotating superconductors. Also a group at the University of Albama claim to have seen gravitational effects from superconductors. So far neither of these effects have been reproduced by other scientists.
So I think the answer to you question is probably no, depending on what exactly you mean by "without the help of mass".
I will have another approach to your question. I guess you are asking about "fast rotating objects" and whether they can duplicate the effects of gravity or not. Well regarding the curvature of spacetime then the answer is clearly no. I don't see a relation between fast rotating object and creating actual gravity. But you said virtual gravity. I will assume you mean by virtual artificial. You can in fact duplicate the effects of gravity by fast rotating objects.
According to the Equivalence principle gravity and acceleration are the same thing. In short, if you were in an elevator accelerating downward with an acceleration equivalent to (g = 9.81 m/s^2), you will feel the elevator floor parting you, and experience the same effect as zero gravity. While in an elevator in space, not under any effect from earth's gravity accelerating towards you feet (upwards), with the acceleration (g = 9.81 m/s^2). You will experience the same effects of the earth's gravity. Bottom line, you can duplicate the effects of gravity by artificial means. Check out this article by wikipedia: http://en.wikipedia.org/wiki/Artificial_gravity
One of the possible ways to duplicate gravity is by centrifugal force. Such is needed in space crafts that will stay a long time in space, to overcome the negative effects of zero gravity on astronauts' health. The centrifugal force can be achieved by the rotation of the space craft, since centrifugal force can be defined as an outward force that draws a rotating body outwards, and where's force there's acceleration. Gravity effects can be duplicated but that's only an effect and not actual gravity that bends spacetime, according to the GR.
On the other hand the rotation of the earth around it's axis is not the cause of its gravity. The gravity of the earth is due to it's mass, and your mass. If your mass "magically" became equivalent to zero, gravity will have no effect on you, even though it's there affecting every thing around you. And that's of coarse hypothetical and impossible to occur. Where there's matter, there's mass, and where there's mass there's gravity.
Wheeler worked on a program a while back that he called "mass without mass", and the general idea was to have something that was localized and from far away looked like it had mass but if you try to find out where the mass is, there is no place, it's all vacuum everywhere.
And there are two general tricks he used. One is like having gravitational waves mutually orbit each other and from far away we see the curvature of the net eaffect, but inside it';s just waves of vacuum spacetime. I think he called them geons, but it's tough to get them to forever orbit each other, so it could just be a temporary effect.
The other trick was nontrivial topology. If you've seen those pictures that look like a funnel on the top and an upside down funnel on the bottom (an Einstein-Rosen bridge) then each funnel connects to a different universe (or a different part of the same universe) but outside that throat it looks like there is a mass there, but there isn't a mass, just a "path" to another (part of the) universe. What's really misleading about those pictures is that it is only showing you the space part of spacetime, so those paths are like the road that is everywhere as opposed to the road you walk (where you walk parts near your start at earlier times than you walk the parts near your destination). If you tried to walk that path through wormhole you can't actually get to the other side. A vacuum spacetime doesn't allow you to travel (through time) through the narrow part of the throat. Even light can't get through.
Classically, gravity requires mass..! But as a consequence of the mass-energy ($mc^2$), energetic objects can curve spacetime too. Anyways, we do take mass or energy into account. This includes photons as well. But due to their negligible energy ($h\nu$), the curvature is very small and can be approximated as there's no curvature at all.
We can put this conclusion based on your question (simply) in a way which is understandable: There's no spacetime curvature in the absence of mass (-energy)..! In your case (in my point of view), fast-rotating objects do curve spacetime (for example, celestial objects).
Because the way you define objects (a visible entity) to be rotating. Objects have mass. If you assume the object to be mass-less, then it's not an object. It's simply mass-less or something that's not massive. And, mass-less particles can't travel below $c$ and hence, they're not visible at all.
Anyways, it is not an object..!