Synchronous data transfer from SQL Server to Oracle
One option with SQL Server is Heterogeneous Database Replication. This works with SQL Server as a source and destination being either of:


  The following non-SQL Server databases are supported as Subscribers to snapshot and transactional publications:  
  
  
  Oracle for all platforms that Oracle supports.  
  IBM DB2 for AS400, MVS, Unix, Linux, and Windows.  
  


Snapshot Replication is best if:


  Using snapshot replication by itself is most appropriate when one or more of the following is true:  
  
  
  Data changes infrequently.  
  It is acceptable to have copies of data that are out of date with respect to the Publisher for a period of time.  
  Replicating small volumes of data.
  A large volume of changes occurs over a short period of time.  
  


Therefore it seems that Transactional Replication is your best option:


  Transactional replication is typically used in server-to-server environments and is appropriate in each of the following cases:  
  
  
  You want incremental changes to be propagated to Subscribers as they occur.
  The application requires low latency between the time changes are made at the Publisher and the changes arrive at the Subscriber.
  The application requires access to intermediate data states. For example, if a row changes five times, transactional replication allows an application to respond to each change (such as firing a trigger), not simply the net data change to the row.  
  The Publisher has a very high volume of insert, update, and delete activity.
  The Publisher or Subscriber is a non-SQL Server database, such as Oracle.
  




You could also look down the Linked Server road and update it with a trigger. I think it could be a lot easier to setup if you have only a single table to sync.

However I will only insert some links as I have never tried it and can't try it right now:


Microsoft How to set up and troubleshoot a linked server to an Oracle database in SQL Server 
MSDN Creating a Linked Server for Oracle in 64bit SQL Server 
MSDN How to get up and running with Oracle and Linked Servers
Technet Oracle Provider for OLE DB


Be careful with the 32/64-bit providers and choose the right one.