Can I inject dependency into migration (using EF-Core code-first migrations)?

There's a way to do what you want to do. In my scenario, I would like to use the database name in the connection string through the DbContext. EF core 2.1.1 is used. The code is modified from here

Create a custom MigrationsAssembly service

using Microsoft.EntityFrameworkCore;
using Microsoft.EntityFrameworkCore.Diagnostics;
using Microsoft.EntityFrameworkCore.Infrastructure;
using Microsoft.EntityFrameworkCore.Internal;
using Microsoft.EntityFrameworkCore.Migrations;
using Microsoft.EntityFrameworkCore.Migrations.Internal;
using System;
using System.Reflection;

public class ContextAwareMigrationsAssembly : MigrationsAssembly
{
    private readonly DbContext context;

    public ContextAwareMigrationsAssembly(
        ICurrentDbContext currentContext,
        IDbContextOptions options,
        IMigrationsIdGenerator idGenerator,
        IDiagnosticsLogger<DbLoggerCategory.Migrations> logger) : base(currentContext, options, idGenerator, logger)
    {
        context = currentContext.Context;
    }

    /// <summary>
    /// Modified from http://weblogs.thinktecture.com/pawel/2018/06/entity-framework-core-changing-db-migration-schema-at-runtime.html
    /// </summary>
    /// <param name="migrationClass"></param>
    /// <param name="activeProvider"></param>
    /// <returns></returns>
    public override Migration CreateMigration(TypeInfo migrationClass, string activeProvider)
    {
        var hasCtorWithDbContext = migrationClass
                .GetConstructor(new[] { typeof(DbContext) }) != null;

        if (hasCtorWithDbContext)
        {
              var instance = (Migration)Activator.CreateInstance(migrationClass.AsType(), context);
              instance.ActiveProvider = activeProvider;
              return instance;
        }

        return base.CreateMigration(migrationClass, activeProvider);
    }
}

Replace the IMigrationAssembly service in your DbContext with your custom class

protected override void OnConfiguring(DbContextOptionsBuilder optionsBuilder)
{
    optionsBuilder.ReplaceService<IMigrationsAssembly, ContextAwareMigrationsAssembly>();
}

Then you can add a DbContext parameter in your migration.

public Migration20180801(DbContext context)
{
    DatabaseName = context.Database.GetDbConnection().Database;
}

In your case, you can replace all the DbContext references with IConfiguration and the relevant instance in the CreateMigration override.

If it is just about your connection-string (is it?), you may want to check this answer, which basically suggests this code in your startup-project (not in your migrations-project):

var myConnectionString = Configuration.GetConnectionString(myConnectionStringName);
services.AddDbContext<MyDbContext>(options => options.UseSqlServer(
    myConnectionString ,
    x => x.MigrationsAssembly(myDbContextAssemblyName)));

you cannot, the migrations need to be able to run outside the context of your application.

Since the Entity-framework command-line tool analyzes your code but does not run the startup.cs class.

Also it is not advisable. your migrations should be plain simple and not depend on anything. if it would, it could lead to major runtime side-effects where missing config could lead to missing tables or columns in production.

additional advise

If it involves a lot of small/equal/manual changes. Best way is to generate your migration file. Why? This way your migration will be deterministic: you know what the outcome will be. If a line in your migration fails, it is simple and clear why that is and easily(er) fixable.