Short answer. No, not personally. Rule 91, Section 1 gives that authority to the Solicitor General or a representative acting on behalf of the Republic, who may petition the court where the deceased last resided (or held estate, if he resided abroad) once someone died intestate leaving no heir entitled to the property.
What the law says
the Solicitor General or his representative in behalf of the Republic of the Philippines, may file a petition in the Court of First Instance of the province where the deceased last resided or in which he had estate, if he resided out of the Philippines, setting forth the facts, and praying that the estate of the deceased be declared escheated.
Rule 91, Section 1 — When and by whom petition filed. Read the full provision →
When escheat comes into play
The rule applies when a person dies intestate, seized of real or personal property in the Philippines, leaving no heir or person by law entitled to the same. It is meant for the situation where property would otherwise sit unclaimed because no one with a legal right to it can be found, not for ordinary intestate estates where heirs simply have not yet come forward to settle things.
Who alone may bring the petition
Filing rests with the Solicitor General or his representative in behalf of the Republic of the Philippines. A private individual, even a concerned neighbor who genuinely cannot locate any heirs, has no standing under this section to start an escheat case; the decision to pursue escheat belongs to the State's own law office. What a private person in that position can do instead is report the situation to the Solicitor General's office, leaving the actual decision on whether to file to that office.
Where the petition is filed
Venue follows the deceased: the petition goes to the court of the province where the deceased last resided or in which he had estate, if he resided out of the Philippines. That anchors the case to the decedent's own connection to the Philippines rather than to wherever the petitioner happens to be. For someone who lived abroad but left property here, the location of that Philippine estate itself becomes the relevant connecting factor for fixing proper venue.
What the petition must ask for
The petition must set forth the relevant facts and pray that the estate be declared escheated, which starts the process the later sections of this rule build out: notice, publication, a hearing, and ultimately a judgment on whether the property should pass to the local government for public benefit. Simply asserting that an estate exists is not enough; the facts supporting intestacy, the absence of known heirs, and the property involved all have to be pleaded with reasonable specificity.