RAM usage is increasing in database server with time RAM usage is increasing in database server with time. When we restart the SQL services it take around 4 GB but after day or two it increases to 11-12 GB and even further.
Application is hosted on separate server. Please suggest what could be the reason.
SQL Server will try and use all the RAM it can get hold of to reduce execution times on queries.

As you have had it running for a day or two, with the increased amount of queries ran it will be using as much RAM that it has available to it.