Malik Obama, a Muslim with Kenyan and US citizenship, also told the BBC that the Republican presidential nominee's proposal for a temporary ban on Muslims entering the US was "common sense".
Mr Trump's plan - pitched as a security measure - has been widely condemned.
Malik Obama has accused the president of turning his back on his family.
He told the BBC's Newsday programme it was "sort of disappointing, somewhat hypocritical" that no representatives of the Obama family from Kenya were attending the Democratic convention, taking place in Philadelphia.
The president, he said, had "made a big deal about his heritage... and now it's a complete blackout".
Malik Obama, who said he was also voting for Mr Trump in order to shift his allegiance from the Democratic Party to the Republican Party.
The president's half-brother has reportedly lived in Washington since the mid-80s.
He is also an aspiring politician in Kenya, running for office in 2013, but failing in his bid to become governor of Siaya county.
Barack Obama was born in Hawaii to an American mother and a Kenyan father who left when he was two years old.
The president visited Kenya for the first time last year since his election in 2009.
Mr Trump, a billionaire property developer, is hoping to succeed him in November's election, where he will face Democratic Party candidate, Hillary Clinton.
Source: Reuters
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