The accepted answer by @DSM has a problem highlighted in the comments:

Be careful with dense because if the values are the same, they get assigned the same rank! – Valerio Ficcadenti

This may cause your code to break if you rely on the uniqueness of (group_ID, rank).

The following code uses argsort within each group and inverts the map, so it does not suffer from the same problem:

df["rank"] = df.groupby("group_ID")["value"].transform(
    lambda x: x.to_frame("value")
    .assign(t=np.arange(x.shape[0]))["t"]
    .map({
        y: x.shape[0] - i
        for i, y in enumerate(x.argsort())
    }))