Angioinvasion remains the important prognostic feature in papillary thyroid cancer (PTC) patients. Literature data indicates several markers that may be associated with oxidative stress and/or angioinvasion. Therefore, we assessed the utility of selected parameters in angioinvasion and metastasis screening in serum of PTC patients. Serum antioxidant capacity (TAC) and sirtuin 3 (SIRT3) levels were decreased (all p < 0.05) and both DNA/RNA oxidative stress damage products (DNA/RNA OSDP) and malondialdehyde (MDA) levels were increased in PTC patients with angioinvasion and metastasis (study group) when compared with PTC patients without these features (all p < 0.01). The highest screening utility in differentiation between angioinvasion and metastasis presence and absence in PTC patients was presented for DNA/RNA OSDP (AUC = 0.71), SIRT3 (AUC = 0.70), and TAC (AUC = 0.67) (all p < 0.05). Our study suggests that peripheral concentration of oxidative stress markers could be useful as angioinvasion and metastasis indicator in PTC patients.