Specific optical rotation is a physical properties for compounds that exist in chiral compounds and its specific and constant and does not change because you should take base line using your blank before analysis of sample to remove solvent effect
The result may be change if you dont do blank sample before analysis of your compound due to the differences in refractive index and density of solvents
Effects of solvents on both optical absorption and optical rotation are well known and documented since long. Even the classic book, Optical Rotary Power by T. Martin Lowry, 1964 lists several cases where the optical rotation changes in magnitude as well as sign with solvent change. Regarding optical absorption: there are several publications reporting shift in position of the peak, as well as change in the strength of absorption with solvent change.
The comment made about measuring blank seems to be off the mark: Yes, optical rotation of the sample has to be measured with respect to the blank as a rule - BUT - in all cases solvents are non chiral, and the optical rotation of the blank solvent filled cell is always close to zero. The blank measurement is more to correct for the spurious rotation introduced by the sample cell and its windows, and not for solvent rotation.
That is the reason why the protocol is to measure the solvent blank and sample in the same sample cell, oriented in the same way on the sample trough. Some polarimeters and the cells used with them have arrangements to ensure that the cell is always positioned in exactly the same way.
If the solvent blank rotation comes out to be significantly different from zero, it either means the solvent has some chiral impurities in it and should be thrown out or the cell windows are defective and should be changed.