We applied social network analysis (SNA) to Tweets mentioning cannabis or opioid-related terms to publicly available COVID-19 related Tweets collected from Jan 21^st to May 3^rd, 2020 (n= 2,558,474 Tweets). We randomly extracted 16,154 Tweets mentioning cannabis and 4,670 Tweets mentioning opioids from the COVID-19 Tweet corpora for our analysis. The cannabis related Tweets created by 6,144 users were disseminated to 280,042,783 users and retweeted 11 times the number of original messages while opioid-related Tweets created by 3,412 users were disseminated to smaller number of users. The opioids Twitter network showed more cohesive online group activities and a cleaner online environment with less disinformation. The cannabis Twitter network showed a less desirable online environment with more disinformation (false information to mislead the public) and stakeholders lacking strong science knowledge. Application of SNA to Tweets provides insights for future online-based drug abuse research during the outbreak.