I have two identical ASP.Net 4.6 MVC project, project 1 is using roslyn complier within the site which is working fine.
c:\\windows\\system32\\inetsrv>C:\\
I just faced a similar issue and fixed it by doing as Huzzi suggested by adding the tags into the main web project's web.config and making sure that you have installed 'Microsoft.CodeDom.Providers.DotNetCompilerPlatform' from nuget.
Try changing the "Target framework" value in your application properties to a newer one.
Got it working now after adding the following to the web.config
<system.codedom>
<compilers>
<compiler language="c#;cs;csharp" extension=".cs"
type="Microsoft.CodeDom.Providers.DotNetCompilerPlatform.CSharpCodeProvider, Microsoft.CodeDom.Providers.DotNetCompilerPlatform, Version=1.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35"
warningLevel="4" compilerOptions="/langversion:6 /nowarn:1659;1699;1701"/>
<compiler language="vb;vbs;visualbasic;vbscript" extension=".vb"
type="Microsoft.CodeDom.Providers.DotNetCompilerPlatform.VBCodeProvider, Microsoft.CodeDom.Providers.DotNetCompilerPlatform, Version=1.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35"
warningLevel="4" compilerOptions="/langversion:14 /nowarn:41008 /define:_MYTYPE=\"Web\" /optionInfer+"/>
</compilers>
</system.codedom>