You are unable to use DATA_COMPRESSION with ALTER INDEX REORGANIZE e.g.
ALTER INDEX CI_c1 ON test_compression_clustered REORGANIZE PARTITION = ALL WITH (DATA_COMPRESSION = PAGE);
However if an index has DATA_COMPRESSION you can perform a reorganize with out losing the data compression:
/* compress index */
ALTER INDEX CI_c1 ON test_compression_clustered REBUILD PARTITION = ALL WITH (DATA_COMPRESSION = PAGE);
/* view compression */
SELECT
OBJECT_NAME(a.object_id) AS table_name
,CASE WHEN a.index_id = 0 THEN 'heap' ELSE b.[name] END AS index_name
,b.type_desc
,a.data_compression_desc
FROM sys.partitions a, sys.indexes b
WHERE 1=1
AND OBJECT_NAME(a.[object_id]) = 'test_compression_clustered'
AND a.[object_id] = b.[object_id]
AND a.index_id = b.index_id
ORDER BY index_name;
/* REORGANIZE */
ALTER INDEX CI_c1 ON test_compression_clustered REORGANIZE;
/* view compression */
SELECT
OBJECT_NAME(a.object_id) AS table_name
,CASE WHEN a.index_id = 0 THEN 'heap' ELSE b.[name] END AS index_name
,b.type_desc
,a.data_compression_desc
FROM sys.partitions a, sys.indexes b
WHERE 1=1
AND OBJECT_NAME(a.[object_id]) = 'test_compression_clustered'
AND a.[object_id] = b.[object_id]
AND a.index_id = b.index_id
ORDER BY index_name;