I found an example of what I wanted to do, written in JS, I was able to make it work by tweaking the code to look like this.
NSMutableURLRequest * request = [[NSMutableURLRequest alloc] initWithURL:[NSURL URLWithString:[NSString stringWithFormat:@"%@?token=%@&action=add-file", [self getBaseURL], token]]];
NSString * boundary = [NSString stringWithFormat:@"AJAX-----------------------%f", [[[NSDate alloc] init] timeIntervalSince1970]];
NSMutableData * body = [NSMutableData alloc];
NSData * torrentFileContents = [[NSFileManager defaultManager] contentsAtPath:fileName];
[request setHTTPMethod:@"POST"];
[request addValue:[NSString stringWithFormat:@"multipart/form-data; boundary=%@", boundary] forHTTPHeaderField:@"Content-Type"];
[body appendData:[[NSString stringWithFormat:@"--%@\r\n", boundary] dataUsingEncoding:NSUTF8StringEncoding]];
[body appendData:[[NSString stringWithFormat:@"Content-Disposition: form-data; name=\"torrent_file\"; filename=\"%@\"\r\n", fileName] dataUsingEncoding:NSUTF8StringEncoding]];
[body appendData:[[NSString stringWithFormat:@"Content-Type: %@\r\n\r\n", @"application/x-bittorrent"] dataUsingEncoding:NSUTF8StringEncoding]];
[body appendData:[NSData dataWithData:torrentFileContents]];
[body appendData:[[NSString stringWithFormat:@"\r\n--%@--\r\n", boundary] dataUsingEncoding:NSUTF8StringEncoding]];
[request setHTTPBody:body];
return request;