Startup.cs

[assembly: WebJobsStartup(typeof(Startup))]
namespace YOUR.NAMESPACE
{
    internal class Startup : IWebJobsStartup
    {
        public void Configure(IWebJobsBuilder builder)
        {
            builder.AddDependencyInjection(ConfigureServices);
        }

        private void ConfigureServices(IServiceCollection services)
        {
            var client = new SendGridClient(Environment.GetEnvironmentVariable("SENDGRID_API_KEY"));
            services.AddSingleton<ISendGridClient>(client);
        }
    }
}