Be cautious: small amounts of turmeric as a spice in food are not a concern, but turmeric/curcumin supplements may add to a blood thinner's bleeding risk, so talk to your doctor or pharmacist before combining them and don't start them on your own if you take warfarin or another anticoagulant.
Turmeric (and its active compound curcumin) may interfere with clotting by decreasing platelet aggregation, so taken as a concentrated supplement it could add to the bleeding risk of anticoagulant and antiplatelet "blood thinners." With warfarin specifically there is an extra concern: curcumin might decrease warfarin's clearance from the body, and warfarin has a narrow therapeutic range, meaning small shifts can tip from effective to dangerous. NHS Wales medicines guidance documents a real case in which a person on warfarin had their INR rise to a level associated with a serious risk of bleeding after starting a product containing turmeric. NHS guidance also names turmeric directly as a herbal product that can potentially increase bleeding risk when combined with antiplatelet blood thinners such as low-dose aspirin. Important context from the same NHS Wales source: information on turmeric's interactions is limited and comes mostly from laboratory or animal studies, so the size of the risk in people is uncertain — but because the consequences of a bleed can be serious, the cautious approach is to check with a professional first.
Culinary turmeric used in cooking is generally not the issue — the concern is concentrated turmeric/curcumin capsules, extracts, or high-dose "bioavailable" formulas. If you take any blood thinner (warfarin, apixaban, rivaroxaban, dabigatran, edoxaban, clopidogrel, or low-dose aspirin), do not start a turmeric supplement without first speaking to your GP, anticoagulant clinic, or pharmacist; if you take warfarin and add turmeric, your INR should be monitored closely. Watch for signs of excess bleeding and seek urgent care for: unusual or prolonged bruising or bleeding, blood in urine or stool, black/tarry stools, vomiting or coughing up blood, nosebleeds or gum bleeding that won't stop, or a severe or sudden headache — in the US call 911 for serious bleeding, or Poison Control at 1-800-222-1222 for guidance. Tell every prescriber and pharmacist about any turmeric/curcumin product you take, and note that NCCIH (NIH) advises checking with your health care provider before any herbal product because herbs and medicines can interact in harmful ways.
This is general reference, not medical advice, and not a guarantee of safety. Interactions depend on your doses, health conditions, and other medicines. Always confirm with your pharmacist or doctor before combining products, and follow the dosing on each label.