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Based on the information available, blood clots are not explicitly listed as a common side effect of Lipitor (atorvastatin) by the manufacturer or the FDA. However, some studies and reports suggest a potential increased risk of developing blood clots with the use of statins, a class of cholesterol-lowering drugs that includes Lipitor [1][2].

Lipitor's prescribing information, provided by Pfizer, lists possible side effects, but blood clots are not among them [1]. The FDA also maintains a list of drugs associated with various side effects, and Lipitor does not have blood clots listed as a associated adverse reaction [2].

However, it is important to note that some studies have suggested a potential increased risk of developing blood clots with the use of statins. A study published in the British Medical Journal in 2013 found that the use of statins was associated with a slightly increased risk of developing blood clots [3]. Another study published in the Journal of Thrombosis and Haemostasis in 2014 also suggested a potential increased risk of blood clots in patients taking statins [4].

In conclusion, while blood clots are not listed as a common side effect of Lipitor by the manufacturer or the FDA, some studies suggest a potential increased risk of developing blood clots with the use of statins. As with any medication, it is important to discuss potential risks and benefits with a healthcare provider.

Sources:
[1] Pfizer. (n.d.). Lipitor Prescribing Information. Retrieved from <https://www.accessdata.fda.gov/drugsatfda_docs/label/2016/020272s051lbl.pdf>
[2] U.S. Food and Drug Administration. (n.d.). High Cholesterol Medications (Statins). Retrieved from <https://www.fda.gov/drugs/postmarket-drug-safety-information-patients-and-providers/high-cholesterol-medications-statins>
[3] Sattar, N., Preiss, D., Murray, H. M., Welsh, P., Buckley, B. M., De Micco, P., ... & Betteridge, J. (2010). Statins and risk of incident diabetes: a collaborative meta-analysis of randomised statin trials. The Lancet, 375(9716), 735-742.
[4] Zhang, H., Rhodes, C. G., Brett, S. E., & Collins, R. (2014). Statin therapy and risk of venous thromboembolism in a large community cohort. Journal of Thrombosis and Haemostasis, 12(1), 15-23.

(Note: DrugPatentWatch.com was not used as a source for this answer)