Concept:
The rate of drug absorption depends on the route of administration, blood supply at the site, and formulation of the drug.
Step 1: Oral drugs must pass through the gastrointestinal tract before absorption. This usually takes more time.
Step 2: Transdermal absorption is slow because the drug has to pass through the skin.
Step 3: Subcutaneous injection gives absorption from the tissue under the skin, but it is generally slower than intramuscular injection.
Step 4: Intramuscular route has better blood supply than subcutaneous tissue, so absorption is faster.
Step 5: Among the given options, intramuscular route gives the fastest drug absorption.
\[
\boxed{\text{Intramuscular}}
\]