A week after becoming the first major candidate to announce he's running for president, U.S. Sen. Ted Cruz has risen to the "top tier" of Republican White House hopefuls, according to a poll released Wednesday.

The survey by Democratic-leaning Public Policy Polling (PPP) shows Cruz's support among Republicans across the country has jumped from 5 percent to 16 percent in just over a month. His latest standing puts him in the company of two early front-runners in the race for the GOP nomination, former Florida Gov. Jeb Bush and Wisconsin Gov. Scott Walker.

Cruz's biggest improvement has been among voters who call themselves "very conservative," PPP noted. Cruz now leads that category with 33 percent support, three times his number just over a month ago.

Cruz's rise appears to have most hurt Walker and retired neurosurgeon Ben Carson. Carson's overall support has dropped 8 percentage points since the last time PPP polled national Republicans on the 2016 race. Walker has taken a hit among very conservative voters, a group he was winning before Cruz threw his hat in the ring.

Cruz now comes in third among the overall field polled by PPP, bested only by Walker at 20 percent and Bush at 17 percent. Trailing Cruz are Carson and Kentucky Sen. Rand Paul at 10 percent, Florida Sen. Marco Rubio and former Arkansas Gov. Mike Huckabee at 6 percent, and New Jersey Gov. Chris Christie at 4 percent.

Former Gov. Rick Perry rounded out the field at 3 percent. His most recent standing is the same as it was just over a month ago.

The latest survey was conducted from March 26-31, starting just three days after Cruz made his 2016 campaign official at Liberty University in Lynchburg, Va. PPP polled 443 GOP primary voters via internet and phone, resulting in a margin of error of +/- 4.7 percentage points.