Update to this answer
In my current python version (3.7, May 2021). The syntax df['Date'].dt.week is printing the following warning: FutureWarning: weekofyear and week have been deprecated, please use DatetimeIndex.isocalendar().week instead
The way to use DatetimeIndex would be: df['week_number'] = pd.DatetimeIndex(df.index).isocalendar().week
Here a small demonstration of its use to return a Series
# Input
time_idx = pd.date_range('2022-01-01', periods=4, freq='H').tz_localize('UTC')
values = [9 , 8, 7, 6]
df1 = pd.DataFrame(data = values, index=time_idx, columns=['vals'])
# FutureWarning: weekofyear and week have been deprecated
df1['week_number'] = df1.index.week
# Using DatetimeIndex.isocalendar().week instead
df2 = pd.DataFrame(data = values, index=time_idx, columns=['vals'])
# Does not throws a warning
df2['week_number'] = pd.DatetimeIndex(df2.index).isocalendar().week
print(df2)