In this paper, we proved a local arithmetic Siegel-Weil formula for a
U
(
1
,
1
)
U(1, 1)
-Shimura variety at a ramified prime, a.k.a. a Kudla-Rapoport conjecture at a ramified case. The formula needs to be modified from the original Kudla-Rapoport conjecture. In the process, we also give an explicit decomposition of the special divisors of the Rapoport-Zink space of unitary type
(
1
,
1
)
(1, 1)
(Krämer model). A key ingredient is to relate the Rapoport-Zink space to the Drinfeld upper plane.