Due to Charles law, the volume of the gas is directly proportional to the temperature of the gas,
$$ V \propto T $$
or
$$ \frac{V}{T} = k $$
Therefore, when the temperature of the gas is increasing, the volume of the gas is increasing as well. And due to the conservation of mass, the temperature will not affect the mass of the gas.
Since density is
$$ \rho = \frac{m}{V} $$
And the mass of the gas is constant
$$ m = const $$
That means the density of the gas always inversely proportional to the volume of the gas, and hence also inversely proportional to the temperature of the gas.
$$ \rho \propto \frac{1}{V} $$
and
$$ \rho \propto \frac{1}{T} $$
Conclusion: When the hot air expands, it becomes less dense than its surrounding air, then the air pressure will exert an upward buoyant force for the hot air to rise.