-  Using Base64
What is Base64
  When you have some binary data that you want to ship across a network, you generally don't do it by just streaming the bits and bytes over the wire in a raw format. Why? because some media are made for streaming text. You never know -- some protocols may interpret your binary data as control characters (like a modem), or your binary data could be screwed up because the underlying protocol might think that you've entered a special character combination (like how FTP translates line endings).
So to get around this, people encode the binary data into characters. Base64 is one of these types of encodings. Why 64? Because you can generally rely on the same 64 characters being present in many character sets, and you can be reasonably confident that your data's going to end up on the other side of the wire uncorrupted.
-- Taken from What is base 64 encoding used for?
So one way of doing it is to put a Base64 string inside your json request and have your app decode it.
 # Your request
 {
    'user':{
     # .... 
         'picture':'GIF89a\xB4\x00\x1F\x00\xE7\xFD....'
     }
 }
Here is what your model could do 
 class User < ActiveRecord::Base
   def convert_from_base64(image_data)
     data = StringIO.new(Base64.decode64(image_data))
     data.class.class_eval { attr_accessor :original_filename, :content_type }
     tmp = Tempfile.new("base64")
     tmp.write(data.read)
     tmp.close
     # only on *nix
     data.content_type = IO.popen(["file", "--brief", "--mime-type",tmp.path], 
        in: :close, err: :close).read.chomp
     data.original_filename = "picture." + data.content_type.split("/").last
     data
   end
 end
 # in your controller
 def create
   image_data = JSON.parse(params[:json])['user']['picture'] #or which ever field it is
   params[:user][:picture] = @user.convert_from_base64(image_data)
   # ....  
 end
But a quick look at POSTMAN tells me you have to do the encoding your self. 
Alternatively
you can just pass a url instead of the data - if the url is pointing to resource available on the net.
require "open-uri"
class User < ActiveRecord::Base
  def picture_from_url(url)
    self.picture = open(url)
  end
end
# then just do 
user.picture_from_url params[:user][:photo_url]
Update
Postman actually allows you to construct a post request with an image attached. Isnt that what you are looking for ?