Para contar los registros de todas las tablas de una base de datos podemos usar el siguiente script:
use base de datos
SELECT [Tables].name AS [TableName],
SUM( [Partitions].[rows] ) AS [TotalRowCount]
FROM sys.tables AS [Tables]
JOIN sys.partitions AS [Partitions]
ON [Tables].[object_id] = [Partitions].[object_id]
AND [Partitions].index_id IN ( 0, 1 )
--WHERE [Tables].name = N'table name' /* uncomment to look for a specific table */
GROUP BY [Tables].name;
Fuente: https://riptutorial.com/sql-server