Cross-country remote working is a tricky thing with taxation. Generally, Germany assumes that if your main residence is in Germany, you need to pay income taxes (as well as mandatory health insurance) there. At the same time, the US IRS will also want to have their taxes. Unless anyone here can chime in with actual experience, you need to get a tax advisor familiar with this to work out specifics (there may be special cases in a double-taxation agreement between the countries).
The cleanest solution is if your employer has an office in Germany anyway and they employ you there. That also tends to simplify the visa question.
In any case, you should be aware that your monthly paycheck will look depressing - gross salaries tend to be a bit lower, taxes and health insurance are withheld and unless you want to move to Germany permanently or for a longer time (ideally reaping many of the benefits like healthcare, childcare, free schooling including university...) this move may not make sense economically.