Solid dispersions provide a key technology to formulate poorly water-soluble drugs, and a main task of early development is appropriate selection of polymer. This study investigates the use of a novel rheology-based approach to evaluate miscibility and interactions of drugs with polymers regarding amorphous solid drug dispersions for oral administration. Tacrolimus was used as model drug and hydroxypropyl cellulose, ethylcellulose, Soluplus®, polyethyleneglycol 6000, Poloxamer-188 (Koliphor-188), and Eudragit® S100 were used as excipients. Solvent-based evaporation methods were used to prepare binary solid dispersions of drug and polymer. Data of the dilute solution viscosimetry were compared with in silico calculations of the Hansen solubility parameter (HSP), as well as phase separation/crystallization data obtained from X-ray diffraction and differential scanning calorimetry. HSP calculations in some cases led to false positive predictions of tacrolimus miscibility with the tested polymers. The novel rheology-based method provided valuable insights into drug-polymer interactions and likely miscibility with polymer. It is a rather fast, inexpensive, and robust analytical approach, which could be used complementary to in silico-based evaluation of polymers in early formulation development, especially in cases of rather large active pharmaceutical ingredients.