Can we trap living cells in optical tweezers? I read that optical tweezers work on the principle of radiation pressure caused due to momentum change of incident light due to refraction from a spherical object. For refraction to happen the object can only be a dielectric material. 
And I read that optical tweezers are used to trap living cells. Is cell a dielectric medium? Does it refract light and not absorb it?
 A: Of course a cell transmits light -- this is how a four-hundred year old optical microscope is used to observe cells.   And in general any medium that transmits light will refract light unless it happens to be exactly the same density as the surrounding medium.
A: yes, a cell is a dielectric material which is one (among) other requirements for optical trapping. Being dielectric does not mean the material can't be absorptive at the same time.
Optical trapping in general means to be able to confine an object into a finite volume. One needs restoring forces in each spatial direction whenever the object tries to leave this volume.
Optical trapping by means of radiation pressure is explained at https://en.wikipedia.org/wiki/Optical_tweezers with the Ray-optic approach. Whenever a ray of light is refracted it causes a momentum transfer from the ray onto the trapped object, even in directions perpendicular!!! to the direction of light propagation (this mechanism allows 3-dimensional confinement) which causes a restoring force in the same direction -> trapping.
Absorption however only allows a momentum transfer in the direction of light propagation and can't confine an object in 3 dimensions. Therefor the absorptive part of the object should be small enough such that the refractive effects dominate.
So all together it means a cell which is trapped in an optical tweezer is a dielectric medium which refracts light and it refracts much more light than it absorbs. However, there is always at least a little absorbtion because no material is 100% transparent.
