You can use: Noemax.WebSockets
This package pulls in all the assemblies required for creating servers
and clients running on .NET Framework (server-side & client-side),
.NET Compact Framework (server-side & client-side), Xamarin.iOS
(server-side & client-side), Xamarin.Android (server-side &
client-side), Windows Phone (client-side), Silverlight (client-side)
and Mono (server-side & client-side).
See here more datails:
https://www.noemax.com/powerwebsockets/

static void Main(string[] args)
{
var client = new WebSocketClient<WebSocketMessagingService>("ws://localhost:8080");
client.Open();
Console.WriteLine(client.Request<string>("Hello", "Hello there !!!"));
Console.WriteLine(client.Request<string>("GoodBye"));
Console.Read();
}