Usually,
yes. A person with
thalassemia minor (trait) can generally donate blood
if they are well and their hemoglobin level meets the blood bank’s minimum on the day of donation. For example, the UK blood service explicitly allows donation for beta-thalassemia trait when hemoglobin is high enough.
UK donor eligibility guidance
Do not take iron just because of thalassemia trait unless iron deficiency has been confirmed by a clinician. The donation center will check hemoglobin first, but local rules vary, so tell them you have thalassemia minor.