The client and server cannot communicate, because they do not possess a common algorithm – ASP.NET C# IIS TLS 1.0 / 1.1 / 1.2 – Win32Exception

There are several other posts about this now and they all point to enabling TLS 1.2. Anything less is unsafe.

You can do this in .NET 3.5 with a patch.
You can do this in .NET 4.0 and 4.5 with a single line of code

ServicePointManager.SecurityProtocol = SecurityProtocolType.Tls12; // .NET 4.5
ServicePointManager.SecurityProtocol = (SecurityProtocolType)3072; // .NET 4.0

In .NET 4.6, it automatically uses TLS 1.2.

See here for more details: .NET support for TLS