Reproducing Ruby OpenSSL private_encrypt output in C#

I have a simple Ruby script that I am using to do a private_encrypt on some HTTP headers to sign a web request that is to be sent to a ruby REST API, the API tests the Base64 encoded string against a Base64 encoded string it generates rather than decoding the Base64 and decrypting the data then testing the original string.

The script I am using is

require "openssl"
require "base64"

path_to_cert = ARGV[0].dup

plain_text = Base64.decode64(ARGV[1].dup)

private_key = OpenSSL::PKey::RSA.new(File.read(path_to_cert))

puts Base64.encode64(private_key.private_encrypt(plain_text))

The fact that the input is Base64 encoded is purely due to linebreaks and spaces in the input argument.

To use this I am having to shell out to ruby using System.Diagnostics.Process and capture the StdOut, while this isn't a major problem and works I'd like to remove the dependency on ruby but I am unable to reproduce the output using the C# RsaCryptoServiceProvider.

If I Base64 Encode the private_encrypt result of "SimpleString" using ruby i consistently get

auReJzoPSW3AhzsfT3EH4rD7lc4y2CJ026xIOiV6kjl2OKIj8GnzrPosoJDg\nSHrvLVKrSxYlegYgJRMx+vaAHSAm7RXrZh5An2SnVuO3qITa2TJ78hTc3bAw\nCDm4i9/4qictjxEFfnPRe6 EYCa4b3dnM5moa1eo9zbQPBa1eS6ItRCX4C0G0\n1tJpQsEvuums363eAhTUAYa6yEWuINLPmE0USW6jfFNnsxw8Nv9SnC+ziomb\n/mwlt9dS5/mzKM8yFMH6hdQYLoqc0QpjT+xaZ1ZyJ6dG5MVG h3JtjIVRTOSd\n+pUU/bo+obEHbrftG8u2uJImLSA+/1e8aapHaa3WNg==

When using the .Net

RsaCryptoServiceProvider.Encrypt("SimpleString", false) 

The result is always a different output due to the fact it is encrypting with the public key.

I have also tried

RsaCryptoServiceProvider.SignData

and while this always yields the same result, it is different to the result from ruby.

Can I use some CryptoAPI directly from .Net that will allow me to achieve the same result as Ruby?