Can I pray tahajjud now?

If Fajr has not yet entered, yes. The whole night, from after Isha until the entry of Fajr, is clear time for tahajjud, and the last third of the night is its most virtuous part. Once Fajr enters, voluntary prayer is withheld: in the Ḥanafī school nothing voluntary is prayed after the entry of Fajr except its two rakʿahs of sunnah, and this restraint continues through sunrise until the sun has fully risen (about twenty minutes after it appears). The live check below tells you exactly where tonight stands for your location.

Rulings differ by madhhab and by what you intend to pray - the live answer below is conditioned on both. Draft pending scholar verification; see the methodology.