No, prior to Visual Studio 2015, you had to install a specific version of Visual Studio in order to target a specific version of SQL Server.
So, you need to use Visual Studio versions 2012, 2015, or 2017* to target SQL Server 2012. Visual Studio 2013 is only compatible with SQL Server 2014.
Starting with Visual Studio 2015, Microsoft introduced the concept of SQL Server targeting, which allowed you to develop for various SQL Server versions without having to install a specific version of Visual Studio. So, you can target SQL Server 2012 in Visual Studio 2015. See the following link for SQL Server Targeting in Visual Studio: https://blogs.msdn.microsoft.com/sqlgardner/2016/08/17/ssdt-vs2015-gotcha-target-server-version-new-feature/
*Note: As of SSDT 15.8.1, Visual Studio 2017 added support for SQL Server 2019 while removing support for SQL Server 2012. If you need to target SQL Server 2012 in Visual Studio 2017, you will need to use a version of SSDT prior to 15.8.1. See the change log here: https://learn.microsoft.com/en-us/sql/ssdt/changelog-for-sql-server-data-tools-ssdt?view=sql-server-2017
Beware of using SQL Server 2012 at this point as Microsoft is slowly phasing it out. In fact, I would be hesitant to use 2014 and would seriously consider going to either 2016 or 2017. Note: SQL Server 2019 is the next version that is coming out.