Does the us currently build nuclear new nuclear warheads?
No. The nuclear weapon stockpile of both major nuclear powers, US and Russia, has been decreasing since the end of cold war. However, when Bush administration came to power it reversed the previous policy of continuing disarmament causing further reductions to cease. Then Bush administration withdrew from the ABM treaty prompting Russia to withdraw from the START 2 nuclear arms limitation treaty. Now both countries are considering new types of nuclear weapons for the first time since the end of cold war, rather than continuing on the path to disarmament that would have included START 2 and the planned START 3 and, eventually, the total elimination of nuclear weapons as was agreed in the NPT treaty.