Forty-eight percent of voters contacted in the state after the convention said they would vote for Biden, while 47 percent said they would back Trump on the presidential ballot, according to the poll, which was released first to the USA Today Network, The Hill reported.
The lead is within the poll's 3.6 percentage point margin of error.
Additionally, the survey showed that 7 percent of Texas voters who backed Trump in 2016 now support Biden, while 3 percent of those who came out for 2016 Democratic nominee Hillary Clinton now support the president.
The findings come as Democrats increasingly set their sights on Texas ahead of November, with a number of polls showing the state could be in play for the party.
A poll from Quinnipiac University released last month also showed Biden leading Trump by 1 percentage point, 45 percent to 44 percent.
The RealClearPolitics polling average shows Trump leading Biden by 3.5 percentage points in Texas.
Trump is set to appear multiple times at the Republican National Convention this week after Biden took the stage at the Democratic National Convention last week.
The president and Republicans could see their own bump in the polls next week, which typically happens following major party conventions.
The Public Policy Polling survey was conducted on Aug. 28 and Aug. 29 among 764 registered voters. The margin of error is plus or minus 3.6 percentage points.