The 56-44 vote rejected an argument from Trump's attorneys that it is unconstitutional to try a former president.
Trump is accused of "inciting insurrection" when Congress was stormed last month.
Thousands gathered in support of false claims that widespread electoral fraud denied Mr Trump victory in the US presidential election.
However Trump is almost certain to be acquitted because only six Republican senators voted to move forward with impeachment, well short of the 17 Republicans whose votes would be needed to convict Trump.
Lawyers for the former president argued it was unconstitutional to put a former president through the process at all and accused Democrats of being politically motivated.
A two-thirds majority is required to convict Trump in the evenly split 100-seat Senate. Tuesday's vote implies loyalty toward the former president in his party remains high enough to avoid a conviction.
However, if convicted, Trump could be barred from holding office again.
As we reported earlier, the US Senate has decided to pause former President Donald Trump’s impeachment trial from Friday evening to Saturday evening this week to honor a request by a Trump attorney who observes the Jewish Sabbath.